(y-2)(y-5)=2y-2

Solution for (y-2)(y-5)=2y-2 equation:

(y-2)(y-5)=2y-2

We move all terms to the left:

(y-2)(y-5)-(2y-2)=0

We get rid of parentheses

(y-2)(y-5)-2y+2=0

We multiply parentheses ..

(+y^2-5y-2y+10)-2y+2=0

We get rid of parentheses

y^2-5y-2y-2y+10+2=0

We add all the numbers together, and all the variables

y^2-9y+12=0

a = 1; b = -9; c = +12;
Δ = b2-4ac
Δ = -92-4·1·12
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{33}}{2*1}=\frac{9-\sqrt{33}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{33}}{2*1}=\frac{9+\sqrt{33}}{2}
$