200q+q^2=6900

Solution for 200q+q^2=6900 equation:

200q+q^2=6900

We move all terms to the left:

200q+q^2-(6900)=0

a = 1; b = 200; c = -6900;
Δ = b2-4ac
Δ = 2002-4·1·(-6900)
Δ = 67600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{67600}=260$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-260}{2*1}=\frac{-460}{2}
=-230
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+260}{2*1}=\frac{60}{2}
=30
$