12(52-3p)p=12

Solution for 12(52-3p)p=12 equation:

12(52-3p)p=12

We move all terms to the left:

12(52-3p)p-(12)=0

We add all the numbers together, and all the variables

12(-3p+52)p-12=0

We multiply parentheses

-36p^2+624p-12=0

a = -36; b = 624; c = -12;
Δ = b2-4ac
Δ = 6242-4·(-36)·(-12)
Δ = 387648
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:

$\sqrt{\Delta}=\sqrt{387648}=\sqrt{576*673}=\sqrt{576}*\sqrt{673}=24\sqrt{673}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(624)-24\sqrt{673}}{2*-36}=\frac{-624-24\sqrt{673}}{-72}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(624)+24\sqrt{673}}{2*-36}=\frac{-624+24\sqrt{673}}{-72}
$