X^2-3x=-2+2x

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

X^2-3X=-2+2X

We move all terms to the left:

X^2-3X-(-2+2X)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

X^2-3X-2X+2=0

We add all the numbers together, and all the variables

X^2-5X+2=0

a = 1; b = -5; c = +2;
Δ = b2-4ac
Δ = -52-4·1·2
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{-(-5)-\sqrt{17}}{2*1}=\frac{5-\sqrt{17}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{17}}{2*1}=\frac{5+\sqrt{17}}{2}
$