1000/(250+p)=p

Solution for 1000/(250+p)=p equation:

1000/(250+p)=p

We move all terms to the left:

1000/(250+p)-(p)=0


Domain of the equation: (250+p)!=0

We move all terms containing p to the left, all other terms to the right

p!=-250

p∈R


We add all the numbers together, and all the variables

1000/(p+250)-p=0

We add all the numbers together, and all the variables

-1p+1000/(p+250)=0

We multiply all the terms by the denominator


-1p*(p+250)+1000=0

We multiply parentheses

-p^2-250p+1000=0

We add all the numbers together, and all the variables

-1p^2-250p+1000=0

a = -1; b = -250; c = +1000;
Δ = b2-4ac
Δ = -2502-4·(-1)·1000
Δ = 66500
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:

$\sqrt{\Delta}=\sqrt{66500}=\sqrt{100*665}=\sqrt{100}*\sqrt{665}=10\sqrt{665}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-250)-10\sqrt{665}}{2*-1}=\frac{250-10\sqrt{665}}{-2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-250)+10\sqrt{665}}{2*-1}=\frac{250+10\sqrt{665}}{-2}
$