3p^2-52=3p+8

Solution for 3p^2-52=3p+8 equation:

3p^2-52=3p+8

We move all terms to the left:

3p^2-52-(3p+8)=0

We get rid of parentheses

3p^2-3p-8-52=0

We add all the numbers together, and all the variables

3p^2-3p-60=0

a = 3; b = -3; c = -60;
Δ = b2-4ac
Δ = -32-4·3·(-60)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-27}{2*3}=\frac{-24}{6}
=-4
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+27}{2*3}=\frac{30}{6}
=5
$