6p^2-4p-180=0

Solution for 6p^2-4p-180=0 equation:

6p^2-4p-180=0

a = 6; b = -4; c = -180;
Δ = b2-4ac
Δ = -42-4·6·(-180)
Δ = 4336
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:

$\sqrt{\Delta}=\sqrt{4336}=\sqrt{16*271}=\sqrt{16}*\sqrt{271}=4\sqrt{271}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{271}}{2*6}=\frac{4-4\sqrt{271}}{12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{271}}{2*6}=\frac{4+4\sqrt{271}}{12}
$