1000p-5000/1000p=0.25

Solution for 1000p-5000/1000p=0.25 equation:

1000p-5000/1000p=0.25

We move all terms to the left:

1000p-5000/1000p-(0.25)=0


Domain of the equation: 1000p!=0

p!=0/1000

p!=0

p∈R


We add all the numbers together, and all the variables

1000p-5000/1000p-0.25=0

We multiply all the terms by the denominator


1000p*1000p-(0.25)*1000p-5000=0

We multiply parentheses

1000p*1000p-250p-5000=0

Wy multiply elements

1000000p^2-250p-5000=0

a = 1000000; b = -250; c = -5000;
Δ = b2-4ac
Δ = -2502-4·1000000·(-5000)
Δ = 20000062500
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:

$\sqrt{\Delta}=\sqrt{20000062500}=\sqrt{62500*320001}=\sqrt{62500}*\sqrt{320001}=250\sqrt{320001}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-250)-250\sqrt{320001}}{2*1000000}=\frac{250-250\sqrt{320001}}{2000000}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-250)+250\sqrt{320001}}{2*1000000}=\frac{250+250\sqrt{320001}}{2000000}
$