2x^2+2x-8=3x-6

Solution for 2x^2+2x-8=3x-6 equation:

2x^2+2x-8=3x-6

We move all terms to the left:

2x^2+2x-8-(3x-6)=0

We get rid of parentheses

2x^2+2x-3x+6-8=0

We add all the numbers together, and all the variables

2x^2-1x-2=0

a = 2; b = -1; c = -2;
Δ = b2-4ac
Δ = -12-4·2·(-2)
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{17}}{2*2}=\frac{1-\sqrt{17}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{17}}{2*2}=\frac{1+\sqrt{17}}{4}
$