4p(p+3)=36

Solution for 4p(p+3)=36 equation:

4p(p+3)=36

We move all terms to the left:

4p(p+3)-(36)=0

We multiply parentheses

4p^2+12p-36=0

a = 4; b = 12; c = -36;
Δ = b2-4ac
Δ = 122-4·4·(-36)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{5}}{2*4}=\frac{-12-12\sqrt{5}}{8}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{5}}{2*4}=\frac{-12+12\sqrt{5}}{8}
$