4x+8=2x^2-2x

Solution for 4x+8=2x^2-2x equation:

4x+8=2x^2-2x

We move all terms to the left:

4x+8-(2x^2-2x)=0

We get rid of parentheses

-2x^2+4x+2x+8=0

We add all the numbers together, and all the variables

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

a = -2; b = 6; c = +8;
Δ = b2-4ac
Δ = 62-4·(-2)·8
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-10}{2*-2}=\frac{-16}{-4}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+10}{2*-2}=\frac{4}{-4}
=-1
$