y^2=-13y

Solution for y^2=-13y equation:

y^2=-13y

We move all terms to the left:

y^2-(-13y)=0

We get rid of parentheses

y^2+13y=0

a = 1; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·1·0
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{-(13)-13}{2*1}=\frac{-26}{2}
=-13
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*1}=\frac{0}{2}
=0
$