2q^2-12q=16

Solution for 2q^2-12q=16 equation:

2q^2-12q=16

We move all terms to the left:

2q^2-12q-(16)=0

a = 2; b = -12; c = -16;
Δ = b2-4ac
Δ = -122-4·2·(-16)
Δ = 272
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:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{17}}{2*2}=\frac{12-4\sqrt{17}}{4}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{17}}{2*2}=\frac{12+4\sqrt{17}}{4}
$