100p-p(^2)=52

Solution for 100p-p(^2)=52 equation:

100p-p(^2)=52

We move all terms to the left:

100p-p(^2)-(52)=0

determiningTheFunctionDomain
-p^2+100p-52=0

We add all the numbers together, and all the variables

-1p^2+100p-52=0

a = -1; b = 100; c = -52;
Δ = b2-4ac
Δ = 1002-4·(-1)·(-52)
Δ = 9792
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:

$\sqrt{\Delta}=\sqrt{9792}=\sqrt{576*17}=\sqrt{576}*\sqrt{17}=24\sqrt{17}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-24\sqrt{17}}{2*-1}=\frac{-100-24\sqrt{17}}{-2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+24\sqrt{17}}{2*-1}=\frac{-100+24\sqrt{17}}{-2}
$