12p^2-57p-15=0

Solution for 12p^2-57p-15=0 equation:

12p^2-57p-15=0

a = 12; b = -57; c = -15;
Δ = b2-4ac
Δ = -572-4·12·(-15)
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-63}{2*12}=\frac{-6}{24}
=-1/4
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+63}{2*12}=\frac{120}{24}
=5
$