50p+50=100/p

Solution for 50p+50=100/p equation:

50p+50=100/p

We move all terms to the left:

50p+50-(100/p)=0


Domain of the equation: p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

50p-(+100/p)+50=0

We get rid of parentheses

50p-100/p+50=0

We multiply all the terms by the denominator


50p*p+50*p-100=0

We add all the numbers together, and all the variables

50p+50p*p-100=0

Wy multiply elements

50p^2+50p-100=0

a = 50; b = 50; c = -100;
Δ = b2-4ac
Δ = 502-4·50·(-100)
Δ = 22500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22500}=150$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-150}{2*50}=\frac{-200}{100}
=-2
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+150}{2*50}=\frac{100}{100}
=1
$