45=-6q^2+51q

Solution for 45=-6q^2+51q equation:

45=-6q^2+51q

We move all terms to the left:

45-(-6q^2+51q)=0

We get rid of parentheses

6q^2-51q+45=0

a = 6; b = -51; c = +45;
Δ = b2-4ac
Δ = -512-4·6·45
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-39}{2*6}=\frac{12}{12}
=1
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+39}{2*6}=\frac{90}{12}
=7+1/2
$