30+2q=13q-0.2q^2

Solution for 30+2q=13q-0.2q^2 equation:

30+2q=13q-0.2q^2

We move all terms to the left:

30+2q-(13q-0.2q^2)=0

We get rid of parentheses

0.2q^2-13q+2q+30=0

We add all the numbers together, and all the variables

0.2q^2-11q+30=0

a = 0.2; b = -11; c = +30;
Δ = b2-4ac
Δ = -112-4·0.2·30
Δ = 97
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{-(-11)-\sqrt{97}}{2*0.2}=\frac{11-\sqrt{97}}{0.4}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{97}}{2*0.2}=\frac{11+\sqrt{97}}{0.4}
$