2q2-2q=100

Solution for 2q2-2q=100 equation:

2q^2-2q=100

We move all terms to the left:

2q^2-2q-(100)=0

a = 2; b = -2; c = -100;
Δ = b2-4ac
Δ = -22-4·2·(-100)
Δ = 804
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:

$\sqrt{\Delta}=\sqrt{804}=\sqrt{4*201}=\sqrt{4}*\sqrt{201}=2\sqrt{201}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{201}}{2*2}=\frac{2-2\sqrt{201}}{4}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{201}}{2*2}=\frac{2+2\sqrt{201}}{4}
$