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

Solution for -y-5+y^2=5y+2y^2 equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

y^2-(5y+2y^2)-1y-5=0

We get rid of parentheses

y^2-2y^2-5y-1y-5=0

We add all the numbers together, and all the variables

-1y^2-6y-5=0

a = -1; b = -6; c = -5;
Δ = b2-4ac
Δ = -62-4·(-1)·(-5)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4}{2*-1}=\frac{2}{-2}
=-1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4}{2*-1}=\frac{10}{-2}
=-5
$