427=-0.006q^2+8.7q-2250

Solution for 427=-0.006q^2+8.7q-2250 equation:

427=-0.006q^2+8.7q-2250

We move all terms to the left:

427-(-0.006q^2+8.7q-2250)=0

We get rid of parentheses

0.006q^2-8.7q+2250+427=0

We add all the numbers together, and all the variables

0.006q^2-8.7q+2677=0

a = 0.006; b = -8.7; c = +2677;
Δ = b2-4ac
Δ = -8.72-4·0.006·2677
Δ = 11.442
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{-(-8.7)-\sqrt{11.442}}{2*0.006}=\frac{8.7-\sqrt{11.442}}{0.012}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8.7)+\sqrt{11.442}}{2*0.006}=\frac{8.7+\sqrt{11.442}}{0.012}
$