55=100-24q+3q^2

Solution for 55=100-24q+3q^2 equation:

55=100-24q+3q^2

We move all terms to the left:

55-(100-24q+3q^2)=0

We get rid of parentheses

-3q^2+24q-100+55=0

We add all the numbers together, and all the variables

-3q^2+24q-45=0

a = -3; b = 24; c = -45;
Δ = b2-4ac
Δ = 242-4·(-3)·(-45)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-6}{2*-3}=\frac{-30}{-6}
=+5
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+6}{2*-3}=\frac{-18}{-6}
=+3
$