6p^2-64p-120=0

Solution for 6p^2-64p-120=0 equation:

6p^2-64p-120=0

a = 6; b = -64; c = -120;
Δ = b2-4ac
Δ = -642-4·6·(-120)
Δ = 6976
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6976}=\sqrt{64*109}=\sqrt{64}*\sqrt{109}=8\sqrt{109}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-8\sqrt{109}}{2*6}=\frac{64-8\sqrt{109}}{12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+8\sqrt{109}}{2*6}=\frac{64+8\sqrt{109}}{12}
$