45=42q-9q^2

Solution for 45=42q-9q^2 equation:

45=42q-9q^2

We move all terms to the left:

45-(42q-9q^2)=0

We get rid of parentheses

9q^2-42q+45=0

a = 9; b = -42; c = +45;
Δ = b2-4ac
Δ = -422-4·9·45
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-12}{2*9}=\frac{30}{18}
=1+2/3
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+12}{2*9}=\frac{54}{18}
=3
$