(100-p)(p-60)=0

Solution for (100-p)(p-60)=0 equation:

(100-p)(p-60)=0

We add all the numbers together, and all the variables

(-1p+100)(p-60)=0

We multiply parentheses ..

(-1p^2+60p+100p-6000)=0

We get rid of parentheses

-1p^2+60p+100p-6000=0

We add all the numbers together, and all the variables

-1p^2+160p-6000=0

a = -1; b = 160; c = -6000;
Δ = b2-4ac
Δ = 1602-4·(-1)·(-6000)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-40}{2*-1}=\frac{-200}{-2}
=+100
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+40}{2*-1}=\frac{-120}{-2}
=+60
$