q^2=-31q

Solution for q^2=-31q equation:

q^2=-31q

We move all terms to the left:

q^2-(-31q)=0

We get rid of parentheses

q^2+31q=0

a = 1; b = 31; c = 0;
Δ = b2-4ac
Δ = 312-4·1·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-31}{2*1}=\frac{-62}{2}
=-31
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+31}{2*1}=\frac{0}{2}
=0
$