6x^2+7x-8=2x-2

Solution for 6x^2+7x-8=2x-2 equation:

6x^2+7x-8=2x-2

We move all terms to the left:

6x^2+7x-8-(2x-2)=0

We get rid of parentheses

6x^2+7x-2x+2-8=0

We add all the numbers together, and all the variables

6x^2+5x-6=0

a = 6; b = 5; c = -6;
Δ = b2-4ac
Δ = 52-4·6·(-6)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-13}{2*6}=\frac{-18}{12}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+13}{2*6}=\frac{8}{12}
=2/3
$