(y-1)2=2y2-11y+15

Solution for (y-1)2=2y2-11y+15 equation:

(y-1)2=2y^2-11y+15

We move all terms to the left:

(y-1)2-(2y^2-11y+15)=0

We multiply parentheses

2y-(2y^2-11y+15)-2=0

We get rid of parentheses

-2y^2+2y+11y-15-2=0

We add all the numbers together, and all the variables

-2y^2+13y-17=0

a = -2; b = 13; c = -17;
Δ = b2-4ac
Δ = 132-4·(-2)·(-17)
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{-(13)-\sqrt{33}}{2*-2}=\frac{-13-\sqrt{33}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{33}}{2*-2}=\frac{-13+\sqrt{33}}{-4}
$