8y+15=y^2

Solution for 8y+15=y^2 equation:

8y+15=y^2

We move all terms to the left:

8y+15-(y^2)=0

determiningTheFunctionDomain
-y^2+8y+15=0

We add all the numbers together, and all the variables

-1y^2+8y+15=0

a = -1; b = 8; c = +15;
Δ = b2-4ac
Δ = 82-4·(-1)·15
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{31}}{2*-1}=\frac{-8-2\sqrt{31}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{31}}{2*-1}=\frac{-8+2\sqrt{31}}{-2}
$