100=100-24q+3q^2

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

100=100-24q+3q^2

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-3q^2+24q=0

a = -3; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·(-3)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*-3}=\frac{-48}{-6}
=+8
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*-3}=\frac{0}{-6}
=0
$