y^2=-14y

Solution for y^2=-14y equation:

y^2=-14y

We move all terms to the left:

y^2-(-14y)=0

We get rid of parentheses

y^2+14y=0

a = 1; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·1·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*1}=\frac{-28}{2}
=-14
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*1}=\frac{0}{2}
=0
$