18-0,5q=330q^2-2q^2

Solution for 18-0,5q=330q^2-2q^2 equation:

18-0.5q=330q^2-2q^2

We move all terms to the left:

18-0.5q-(330q^2-2q^2)=0

We get rid of parentheses

-330q^2+2q^2-0.5q+18=0

We add all the numbers together, and all the variables

-328q^2-0.5q+18=0

a = -328; b = -0.5; c = +18;
Δ = b2-4ac
Δ = -0.52-4·(-328)·18
Δ = 23616.25
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{-(-0.5)-\sqrt{23616.25}}{2*-328}=\frac{0.5-\sqrt{23616.25}}{-656}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.5)+\sqrt{23616.25}}{2*-328}=\frac{0.5+\sqrt{23616.25}}{-656}
$