0=0.01q^2+0.30q-105.91

Solution for 0=0.01q^2+0.30q-105.91 equation:

0=0.01q^2+0.30q-105.91

We move all terms to the left:

0-(0.01q^2+0.30q-105.91)=0

We add all the numbers together, and all the variables

-(0.01q^2+0.30q-105.91)=0

We get rid of parentheses

-0.01q^2-0.30q+105.91=0

We add all the numbers together, and all the variables

-0.01q^2-0.3q+105.91=0

a = -0.01; b = -0.3; c = +105.91;
Δ = b2-4ac
Δ = -0.32-4·(-0.01)·105.91
Δ = 4.3264
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-0.3)-\sqrt{4.3264}}{2*-0.01}=\frac{0.3-\sqrt{4.3264}}{-0.02}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.3)+\sqrt{4.3264}}{2*-0.01}=\frac{0.3+\sqrt{4.3264}}{-0.02}
$