6q^2-24q-5=0

Solution for 6q^2-24q-5=0 equation:

6q^2-24q-5=0

a = 6; b = -24; c = -5;
Δ = b2-4ac
Δ = -242-4·6·(-5)
Δ = 696
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:

$\sqrt{\Delta}=\sqrt{696}=\sqrt{4*174}=\sqrt{4}*\sqrt{174}=2\sqrt{174}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{174}}{2*6}=\frac{24-2\sqrt{174}}{12}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{174}}{2*6}=\frac{24+2\sqrt{174}}{12}
$