-8.5+7.5q+2q^2=0

Solution for -8.5+7.5q+2q^2=0 equation:

-8.5+7.5q+2q^2=0

a = 2; b = 7.5; c = -8.5;
Δ = b2-4ac
Δ = 7.52-4·2·(-8.5)
Δ = 124.25
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{-(7.5)-\sqrt{124.25}}{2*2}=\frac{-7.5-\sqrt{124.25}}{4}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7.5)+\sqrt{124.25}}{2*2}=\frac{-7.5+\sqrt{124.25}}{4}
$