3x-2=2x^2-2x

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

3x-2=2x^2-2x

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2+5x-2=0

a = -2; b = 5; c = -2;
Δ = b2-4ac
Δ = 52-4·(-2)·(-2)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3}{2*-2}=\frac{-8}{-4}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3}{2*-2}=\frac{-2}{-4}
=1/2
$