200/p=5p-30

Solution for 200/p=5p-30 equation:

200/p=5p-30

We move all terms to the left:

200/p-(5p-30)=0


Domain of the equation: p!=0

p∈R


We get rid of parentheses

200/p-5p+30=0

We multiply all the terms by the denominator


-5p*p+30*p+200=0

We add all the numbers together, and all the variables

30p-5p*p+200=0

Wy multiply elements

-5p^2+30p+200=0

a = -5; b = 30; c = +200;
Δ = b2-4ac
Δ = 302-4·(-5)·200
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-70}{2*-5}=\frac{-100}{-10}
=+10
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+70}{2*-5}=\frac{40}{-10}
=-4
$