Q(x)=200x+6x^2

Solution for Q(x)=200x+6x^2 equation:

(Q)=200Q+6Q^2

We move all terms to the left:

(Q)-(200Q+6Q^2)=0

We get rid of parentheses

-6Q^2-200Q+Q=0

We add all the numbers together, and all the variables

-6Q^2-199Q=0

a = -6; b = -199; c = 0;
Δ = b2-4ac
Δ = -1992-4·(-6)·0
Δ = 39601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{39601}=199$
$Q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-199)-199}{2*-6}=\frac{0}{-12}
=0
$
$Q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-199)+199}{2*-6}=\frac{398}{-12}
=-33+1/6
$