L=-0.2q^2+11q-30

Solution for L=-0.2q^2+11q-30 equation:

=-0.2L^2+11L-30

We move all terms to the left:

-(-0.2L^2+11L-30)=0

We get rid of parentheses

0.2L^2-11L+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:
$L_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$L_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$L_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{97}}{2*0.2}=\frac{11-\sqrt{97}}{0.4}
$
$L_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{97}}{2*0.2}=\frac{11+\sqrt{97}}{0.4}
$