8k2-24k-60=0

Solution for 8k2-24k-60=0 equation:

8k^2-24k-60=0

a = 8; b = -24; c = -60;
Δ = b2-4ac
Δ = -242-4·8·(-60)
Δ = 2496
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2496}=\sqrt{64*39}=\sqrt{64}*\sqrt{39}=8\sqrt{39}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{39}}{2*8}=\frac{24-8\sqrt{39}}{16}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{39}}{2*8}=\frac{24+8\sqrt{39}}{16}
$