Question

Solve the equation –3x2 - 5x + 2 = 4 using the quadratic formula.-b+Vb2-4ac2a

Answer 1

-1 and -2/3

Explanation:

We have the following equation:

`-3x^2\: -\: 5x\: +\: 2\: =\: 4`

We rearrange the equation and it looks like this:

`\begin{gathered} -3x^2\: -\: 5x\: +\: 2\: -4=\: 4-4 \\ -3x^2\: -\: 5x\: -2=0 \end{gathered}`

We apply the quadratic formula which is the following:

`\begin{gathered} x_(1,2)=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{ in this case} \\ a=-3 \\ b=-5 \\ c=-2 \end{gathered}`

we replace and calculate the values of x:

`\begin{gathered} x_(1,2)=\frac{-(-5)\pm\sqrt[]{(-5)^2-4\cdot(-3)\cdot(-2)}}{2\cdot(-3)} \\ x_(1,2)=(5\pm1)/(-6) \\ x_1=(5+1)/(-6)=(6)/(-6)=-1 \\ x_2=(5-1)/(-6)=(4)/(-6)=-(2)/(3) \end{gathered}`

Therefore the solution of the equation is -1 and -2/3