9q^2=-9q

Solution for 9q^2=-9q equation:

9q^2=-9q

We move all terms to the left:

9q^2-(-9q)=0

We get rid of parentheses

9q^2+9q=0

a = 9; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·9·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*9}=\frac{-18}{18}
=-1
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*9}=\frac{0}{18}
=0
$