Explanation:
4/5x-3=3/10x+7
We move all terms to the left:
4/5x-3-(3/10x+7)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 10x+7)!=0
x∈R
We get rid of parentheses
4/5x-3/10x-7-3=0
We calculate fractions
40x/50x^2+(-15x)/50x^2-7-3=0
We add all the numbers together, and all the variables
40x/50x^2+(-15x)/50x^2-10=0
We multiply all the terms by the denominator
40x+(-15x)-10*50x^2=0
Wy multiply elements
-500x^2+40x+(-15x)=0
We get rid of parentheses
-500x^2+40x-15x=0
We add all the numbers together, and all the variables
-500x^2+25x=0
a = -500; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-500)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
x1=−b−Δ√2ax2=−b+Δ√2a
Δ−−√=625−−−√=25
x1=−b−Δ√2a=−(25)−252∗−500=−50−1000=1/20
x2=−b+Δ√2a=−(25)+252∗−500=0−1000=0