200q=2q^2

Solution for 200q=2q^2 equation:

200q=2q^2

We move all terms to the left:

200q-(2q^2)=0

determiningTheFunctionDomain
-2q^2+200q=0

a = -2; b = 200; c = 0;
Δ = b2-4ac
Δ = 2002-4·(-2)·0
Δ = 40000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40000}=200$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-200}{2*-2}=\frac{-400}{-4}
=+100
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+200}{2*-2}=\frac{0}{-4}
=0
$