(y-2)2=2y2-6y-11

Solution for (y-2)2=2y2-6y-11 equation:

(y-2)2=2y^2-6y-11

We move all terms to the left:

(y-2)2-(2y^2-6y-11)=0

We multiply parentheses

2y-(2y^2-6y-11)-4=0

We get rid of parentheses

-2y^2+2y+6y+11-4=0

We add all the numbers together, and all the variables

-2y^2+8y+7=0

a = -2; b = 8; c = +7;
Δ = b2-4ac
Δ = 82-4·(-2)·7
Δ = 120
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{30}}{2*-2}=\frac{-8-2\sqrt{30}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{30}}{2*-2}=\frac{-8+2\sqrt{30}}{-4}
$