106.20-0.20q=0.01q^2+5.19

Solution for 106.20-0.20q=0.01q^2+5.19 equation:

106.20-0.20q=0.01q^2+5.19

We move all terms to the left:

106.20-0.20q-(0.01q^2+5.19)=0

We add all the numbers together, and all the variables

-0.2q-(0.01q^2+5.19)+106.2=0

We get rid of parentheses

-0.01q^2-0.2q-5.19+106.2=0

We add all the numbers together, and all the variables

-0.01q^2-0.2q+101.01=0

a = -0.01; b = -0.2; c = +101.01;
Δ = b2-4ac
Δ = -0.22-4·(-0.01)·101.01
Δ = 4.0804
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{-(-0.2)-\sqrt{4.0804}}{2*-0.01}=\frac{0.2-\sqrt{4.0804}}{-0.02}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.2)+\sqrt{4.0804}}{2*-0.01}=\frac{0.2+\sqrt{4.0804}}{-0.02}
$