p(120-4p)=600

Solution for p(120-4p)=600 equation:

p(120-4p)=600

We move all terms to the left:

p(120-4p)-(600)=0

We add all the numbers together, and all the variables

p(-4p+120)-600=0

We multiply parentheses

-4p^2+120p-600=0

a = -4; b = 120; c = -600;
Δ = b2-4ac
Δ = 1202-4·(-4)·(-600)
Δ = 4800
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:

$\sqrt{\Delta}=\sqrt{4800}=\sqrt{1600*3}=\sqrt{1600}*\sqrt{3}=40\sqrt{3}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-40\sqrt{3}}{2*-4}=\frac{-120-40\sqrt{3}}{-8}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+40\sqrt{3}}{2*-4}=\frac{-120+40\sqrt{3}}{-8}
$