5y^2=-33y

Solution for 5y^2=-33y equation:

5y^2=-33y

We move all terms to the left:

5y^2-(-33y)=0

We get rid of parentheses

5y^2+33y=0

a = 5; b = 33; c = 0;
Δ = b2-4ac
Δ = 332-4·5·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-33}{2*5}=\frac{-66}{10}
=-6+3/5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+33}{2*5}=\frac{0}{10}
=0
$