X^2-2x+2=5x-4

Solution for X^2-2x+2=5x-4 equation:

X^2-2X+2=5X-4

We move all terms to the left:

X^2-2X+2-(5X-4)=0

We get rid of parentheses

X^2-2X-5X+4+2=0

We add all the numbers together, and all the variables

X^2-7X+6=0

a = 1; b = -7; c = +6;
Δ = b2-4ac
Δ = -72-4·1·6
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-5}{2*1}=\frac{2}{2}
=1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+5}{2*1}=\frac{12}{2}
=6
$