(3p-37)(2p-48)=180

Solution for (3p-37)(2p-48)=180 equation:

(3p-37)(2p-48)=180

We move all terms to the left:

(3p-37)(2p-48)-(180)=0

We multiply parentheses ..

(+6p^2-144p-74p+1776)-180=0

We get rid of parentheses

6p^2-144p-74p+1776-180=0

We add all the numbers together, and all the variables

6p^2-218p+1596=0

a = 6; b = -218; c = +1596;
Δ = b2-4ac
Δ = -2182-4·6·1596
Δ = 9220
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:

$\sqrt{\Delta}=\sqrt{9220}=\sqrt{4*2305}=\sqrt{4}*\sqrt{2305}=2\sqrt{2305}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-218)-2\sqrt{2305}}{2*6}=\frac{218-2\sqrt{2305}}{12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-218)+2\sqrt{2305}}{2*6}=\frac{218+2\sqrt{2305}}{12}
$