8+3y=y^2

Solution for 8+3y=y^2 equation:

8+3y=y^2

We move all terms to the left:

8+3y-(y^2)=0

determiningTheFunctionDomain
-y^2+3y+8=0

We add all the numbers together, and all the variables

-1y^2+3y+8=0

a = -1; b = 3; c = +8;
Δ = b2-4ac
Δ = 32-4·(-1)·8
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{41}}{2*-1}=\frac{-3-\sqrt{41}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{41}}{2*-1}=\frac{-3+\sqrt{41}}{-2}
$