Answer:
905}}{56}
Explanation:
How to solve your problem
Quadratic formula
1
Combine multiplied terms into a single fraction
x+\frac{2}{3}x-(x-5)=10x+\frac{-5}{x}
x+\frac{2x}{3}-(x-5)=10x+\frac{-5}{x}
2
Distribute
x+\frac{2x}{3}-\left( x-5\right) =10x+\frac{-5}{x}
x+\frac{2x}{3}-x+5=10x+\frac{-5}{x}
3
Combine like terms
\textcolor{#B14BA5}{x}+\frac{2x}{3}\textcolor{#B14BA5}{-x}+5=10x+\frac{-5}{x}
\textcolor{#B14BA5}{\frac{2x}{3}}+5=10x+\frac{-5}{x}
4
Find common denominator
\frac{2x}{3}+5=10x+\frac{-5}{x}
\frac{2x}{3}+\frac{3\cdot 5}{3}=10x+\frac{-5}{x}
5
Combine fractions with common denominator
\frac{2x}{3}+\frac{3\cdot 5}{3}=10x+\frac{-5}{x}
\frac{2x+3\cdot 5}{3}=10x+\frac{-5}{x}
6
Multiply the numbers
\frac{2x+\textcolor{#B14BA5}{3}\cdot \textcolor{#B14BA5}{5}}{3}=10x+\frac{-5}{x}
\frac{2x+\textcolor{#B14BA5}{15}}{3}=10x+\frac{-5}{x}
7
Find common denominator
\frac{2x+15}{3}=10x+\frac{-5}{x}
\frac{2x+15}{3}=\frac{x\cdot 10x}{x}+\frac{-5}{x}
8
Combine fractions with common denominator
\frac{2x+15}{3}=\frac{x\cdot 10x}{x}+\frac{-5}{x}
\frac{2x+15}{3}=\frac{x\cdot 10x-5}{x}
9
Re-order terms so constants are on the left
\frac{2x+15}{3}=\frac{x\cdot \textcolor{#B14BA5}{10}x-5}{x}
\frac{2x+15}{3}=\frac{\textcolor{#B14BA5}{10}xx-5}{x}
10
Combine exponents
\frac{2x+15}{3}=\frac{10\textcolor{#B14BA5}{x}\textcolor{#B14BA5}{x}-5}{x}
\frac{2x+15}{3}=\frac{10\textcolor{#B14BA5}{x^{2}}-5}{x}
11
Multiply all terms by the same value to eliminate fraction denominators
\frac{2x+15}{3}=\frac{10x^{2}-5}{x}
3x\cdot \frac{2x+15}{3}=3x\cdot \frac{10x^{2}-5}{x}
12
Cancel multiplied terms that are in the denominator
3x\cdot \frac{2x+15}{3}=3x\cdot \frac{10x^{2}-5}{x}
x(2x+15)=3\left( 10x^{2}-5\right)
13
Distribute
\textcolor{#B14BA5}{x(2x+15)}=3\left( 10x^{2}-5\right)
\textcolor{#B14BA5}{2x^{2}+15x}=3\left( 10x^{2}-5\right)
14
Distribute
2x^{2}+15x=\textcolor{#B14BA5}{3\left( 10x^{2}-5\right) }
2x^{2}+15x=\textcolor{#B14BA5}{30x^{2}-15}
15
Move terms to the left side
2x^{2}+15x=30x^{2}-15
2x^{2}+15x-\left( 30x^{2}-15\right) =0
16
Distribute
2x^{2}+15x-\left( 30x^{2}-15\right) =0
2x^{2}+15x-30x^{2}+15=0
17
Combine like terms
\textcolor{#B14BA5}{2x^{2}}+15x\textcolor{#B14BA5}{-30x^{2}}+15=0
\textcolor{#B14BA5}{-28x^{2}}+15x+15=0
18
Common factor
-28x^{2}+15x+15=0
-\left( 28x^{2}-15x-15\right) =0
19
Divide both sides by the same factor
-\left( 28x^{2}-15x-15\right) =0
28x^{2}-15x-15=0
20
Use the quadratic formula
x=\frac{-\textcolor{#D24040}{b}\pm \sqrt{\textcolor{#D24040}{b}^{2}-4\textcolor{#B14BA5}{a}\textcolor{#3172E0}{c}}}{2\textcolor{#B14BA5}{a}}
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.
28x^{2}-15x-15=0
a=\textcolor{#B14BA5}{28}
b=\textcolor{#D24040}{-15}
c=\textcolor{#3172E0}{-15}
x=\frac{-(\textcolor{#D24040}{-15})\pm \sqrt{(\textcolor{#D24040}{-15})^{2}-4\cdot \textcolor{#B14BA5}{28}(\textcolor{#3172E0}{-15})}}{2\cdot \textcolor{#B14BA5}{28}}
21
Simplify
Evaluate the exponent
Multiply the numbers
Add the numbers
Multiply the numbers
x=\frac{15\pm \sqrt{1905}}{56}
22
Separate the equations
To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.
x=\frac{15+\sqrt{1905}}{56}
x=\frac{15-\sqrt{1905}}{56}
23
Solve
Rearrange and isolate the variable to find each solution
x=\frac{15+\sqrt{1905}}{56}