3p^2-3p=13

Solution for 3p^2-3p=13 equation:

3p^2-3p=13

We move all terms to the left:

3p^2-3p-(13)=0

a = 3; b = -3; c = -13;
Δ = b2-4ac
Δ = -32-4·3·(-13)
Δ = 165
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{165}}{2*3}=\frac{3-\sqrt{165}}{6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{165}}{2*3}=\frac{3+\sqrt{165}}{6}
$