-(y2-2)=y2-5-2y

Solution for -(y2-2)=y2-5-2y equation:

-(y2-2)=y2-5-2y

We move all terms to the left:

-(y2-2)-(y2-5-2y)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -2; b = 2; c = +7;
Δ = b2-4ac
Δ = 22-4·(-2)·7
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{15}}{2*-2}=\frac{-2-2\sqrt{15}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{15}}{2*-2}=\frac{-2+2\sqrt{15}}{-4}
$