43p^2+156p-48=0

Solution for 43p^2+156p-48=0 equation:

43p^2+156p-48=0

a = 43; b = 156; c = -48;
Δ = b2-4ac
Δ = 1562-4·43·(-48)
Δ = 32592
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:

$\sqrt{\Delta}=\sqrt{32592}=\sqrt{16*2037}=\sqrt{16}*\sqrt{2037}=4\sqrt{2037}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(156)-4\sqrt{2037}}{2*43}=\frac{-156-4\sqrt{2037}}{86}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(156)+4\sqrt{2037}}{2*43}=\frac{-156+4\sqrt{2037}}{86}
$