6q(q-9)=0

Solution for 6q(q-9)=0 equation:

6q(q-9)=0

We multiply parentheses

6q^2-54q=0

a = 6; b = -54; c = 0;
Δ = b2-4ac
Δ = -542-4·6·0
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-54}{2*6}=\frac{0}{12}
=0
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+54}{2*6}=\frac{108}{12}
=9
$