200p-5000/200p=3

Solution for 200p-5000/200p=3 equation:

200p-5000/200p=3

We move all terms to the left:

200p-5000/200p-(3)=0


Domain of the equation: 200p!=0

p!=0/200

p!=0

p∈R


We multiply all the terms by the denominator


200p*200p-3*200p-5000=0

Wy multiply elements

40000p^2-600p-5000=0

a = 40000; b = -600; c = -5000;
Δ = b2-4ac
Δ = -6002-4·40000·(-5000)
Δ = 800360000
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:

$\sqrt{\Delta}=\sqrt{800360000}=\sqrt{40000*20009}=\sqrt{40000}*\sqrt{20009}=200\sqrt{20009}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-600)-200\sqrt{20009}}{2*40000}=\frac{600-200\sqrt{20009}}{80000}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-600)+200\sqrt{20009}}{2*40000}=\frac{600+200\sqrt{20009}}{80000}
$