4y^2=-32y

Solution for 4y^2=-32y equation:

4y^2=-32y

We move all terms to the left:

4y^2-(-32y)=0

We get rid of parentheses

4y^2+32y=0

a = 4; b = 32; c = 0;
Δ = b2-4ac
Δ = 322-4·4·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32}{2*4}=\frac{-64}{8}
=-8
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32}{2*4}=\frac{0}{8}
=0
$