2q2-8q=40

Solution for 2q2-8q=40 equation:

2q^2-8q=40

We move all terms to the left:

2q^2-8q-(40)=0

a = 2; b = -8; c = -40;
Δ = b2-4ac
Δ = -82-4·2·(-40)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{6}}{2*2}=\frac{8-8\sqrt{6}}{4}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{6}}{2*2}=\frac{8+8\sqrt{6}}{4}
$