y^2-8=32-3y

Solution for y^2-8=32-3y equation:

y^2-8=32-3y

We move all terms to the left:

y^2-8-(32-3y)=0

We add all the numbers together, and all the variables

y^2-(-3y+32)-8=0

We get rid of parentheses

y^2+3y-32-8=0

We add all the numbers together, and all the variables

y^2+3y-40=0

a = 1; b = 3; c = -40;
Δ = b2-4ac
Δ = 32-4·1·(-40)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-13}{2*1}=\frac{-16}{2}
=-8
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+13}{2*1}=\frac{10}{2}
=5
$