2p(p+1)=36

Solution for 2p(p+1)=36 equation:

2p(p+1)=36

We move all terms to the left:

2p(p+1)-(36)=0

We multiply parentheses

2p^2+2p-36=0

a = 2; b = 2; c = -36;
Δ = b2-4ac
Δ = 22-4·2·(-36)
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{73}}{2*2}=\frac{-2-2\sqrt{73}}{4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{73}}{2*2}=\frac{-2+2\sqrt{73}}{4}
$