15q=-q^2+10000

Solution for 15q=-q^2+10000 equation:

15q=-q^2+10000

We move all terms to the left:

15q-(-q^2+10000)=0

We get rid of parentheses

q^2+15q-10000=0

a = 1; b = 15; c = -10000;
Δ = b2-4ac
Δ = 152-4·1·(-10000)
Δ = 40225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{40225}=\sqrt{25*1609}=\sqrt{25}*\sqrt{1609}=5\sqrt{1609}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5\sqrt{1609}}{2*1}=\frac{-15-5\sqrt{1609}}{2}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5\sqrt{1609}}{2*1}=\frac{-15+5\sqrt{1609}}{2}
$