4q^2-16q=24

Solution for 4q^2-16q=24 equation:

4q^2-16q=24

We move all terms to the left:

4q^2-16q-(24)=0

a = 4; b = -16; c = -24;
Δ = b2-4ac
Δ = -162-4·4·(-24)
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{10}}{2*4}=\frac{16-8\sqrt{10}}{8}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{10}}{2*4}=\frac{16+8\sqrt{10}}{8}
$