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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2+10x-11=0

a = 1; b = 10; c = -11;
Δ = b2-4ac
Δ = 102-4·1·(-11)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-12}{2*1}=\frac{-22}{2}
=-11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+12}{2*1}=\frac{2}{2}
=1
$