q^2+20q=8400

Solution for q^2+20q=8400 equation:

q^2+20q=8400

We move all terms to the left:

q^2+20q-(8400)=0

a = 1; b = 20; c = -8400;
Δ = b2-4ac
Δ = 202-4·1·(-8400)
Δ = 34000
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:

$\sqrt{\Delta}=\sqrt{34000}=\sqrt{400*85}=\sqrt{400}*\sqrt{85}=20\sqrt{85}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20\sqrt{85}}{2*1}=\frac{-20-20\sqrt{85}}{2}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20\sqrt{85}}{2*1}=\frac{-20+20\sqrt{85}}{2}
$