12p^2-6p-15=0

Solution for 12p^2-6p-15=0 equation:

12p^2-6p-15=0

a = 12; b = -6; c = -15;
Δ = b2-4ac
Δ = -62-4·12·(-15)
Δ = 756
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:

$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{21}}{2*12}=\frac{6-6\sqrt{21}}{24}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{21}}{2*12}=\frac{6+6\sqrt{21}}{24}
$