(3p)(2p+5)=180

Solution for (3p)(2p+5)=180 equation:

(3p)(2p+5)=180

We move all terms to the left:

(3p)(2p+5)-(180)=0

We multiply parentheses

6p^2+15p-180=0

a = 6; b = 15; c = -180;
Δ = b2-4ac
Δ = 152-4·6·(-180)
Δ = 4545
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:

$\sqrt{\Delta}=\sqrt{4545}=\sqrt{9*505}=\sqrt{9}*\sqrt{505}=3\sqrt{505}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{505}}{2*6}=\frac{-15-3\sqrt{505}}{12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{505}}{2*6}=\frac{-15+3\sqrt{505}}{12}
$