y^2+6y+15=2y^2+6y-10

Solution for y^2+6y+15=2y^2+6y-10 equation:

y^2+6y+15=2y^2+6y-10

We move all terms to the left:

y^2+6y+15-(2y^2+6y-10)=0

We get rid of parentheses

y^2-2y^2+6y-6y+10+15=0

We add all the numbers together, and all the variables

-1y^2+25=0

a = -1; b = 0; c = +25;
Δ = b2-4ac
Δ = 02-4·(-1)·25
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10}{2*-1}=\frac{-10}{-2}
=+5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10}{2*-1}=\frac{10}{-2}
=-5
$