2y+5+y^2=-6y+2y^2

Solution for 2y+5+y^2=-6y+2y^2 equation:

2y+5+y^2=-6y+2y^2

We move all terms to the left:

2y+5+y^2-(-6y+2y^2)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1y^2+8y+5=0

a = -1; b = 8; c = +5;
Δ = b2-4ac
Δ = 82-4·(-1)·5
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{21}}{2*-1}=\frac{-8-2\sqrt{21}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{21}}{2*-1}=\frac{-8+2\sqrt{21}}{-2}
$