p(3p+2)=76

Solution for p(3p+2)=76 equation:

p(3p+2)=76

We move all terms to the left:

p(3p+2)-(76)=0

We multiply parentheses

3p^2+2p-76=0

a = 3; b = 2; c = -76;
Δ = b2-4ac
Δ = 22-4·3·(-76)
Δ = 916
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:

$\sqrt{\Delta}=\sqrt{916}=\sqrt{4*229}=\sqrt{4}*\sqrt{229}=2\sqrt{229}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{229}}{2*3}=\frac{-2-2\sqrt{229}}{6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{229}}{2*3}=\frac{-2+2\sqrt{229}}{6}
$