12p2+8p-77=0

Solution for 12p2+8p-77=0 equation:

12p^2+8p-77=0

a = 12; b = 8; c = -77;
Δ = b2-4ac
Δ = 82-4·12·(-77)
Δ = 3760
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:

$\sqrt{\Delta}=\sqrt{3760}=\sqrt{16*235}=\sqrt{16}*\sqrt{235}=4\sqrt{235}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{235}}{2*12}=\frac{-8-4\sqrt{235}}{24}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{235}}{2*12}=\frac{-8+4\sqrt{235}}{24}
$