2q2-24q-48=0

Solution for 2q2-24q-48=0 equation:

2q^2-24q-48=0

a = 2; b = -24; c = -48;
Δ = b2-4ac
Δ = -242-4·2·(-48)
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{15}}{2*2}=\frac{24-8\sqrt{15}}{4}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{15}}{2*2}=\frac{24+8\sqrt{15}}{4}
$