q=-3q^2-10q+15400

Solution for q=-3q^2-10q+15400 equation:

q=-3q^2-10q+15400

We move all terms to the left:

q-(-3q^2-10q+15400)=0

We get rid of parentheses

3q^2+10q+q-15400=0

We add all the numbers together, and all the variables

3q^2+11q-15400=0

a = 3; b = 11; c = -15400;
Δ = b2-4ac
Δ = 112-4·3·(-15400)
Δ = 184921
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{184921}}{2*3}=\frac{-11-\sqrt{184921}}{6}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{184921}}{2*3}=\frac{-11+\sqrt{184921}}{6}
$