3p(p+3)+9p=6

Solution for 3p(p+3)+9p=6 equation:

3p(p+3)+9p=6

We move all terms to the left:

3p(p+3)+9p-(6)=0

We add all the numbers together, and all the variables

9p+3p(p+3)-6=0

We multiply parentheses

3p^2+9p+9p-6=0

We add all the numbers together, and all the variables

3p^2+18p-6=0

a = 3; b = 18; c = -6;
Δ = b2-4ac
Δ = 182-4·3·(-6)
Δ = 396
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:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{11}}{2*3}=\frac{-18-6\sqrt{11}}{6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{11}}{2*3}=\frac{-18+6\sqrt{11}}{6}
$