550-(2/p)=5p

Solution for 550-(2/p)=5p equation:

550-(2/p)=5p

We move all terms to the left:

550-(2/p)-(5p)=0


Domain of the equation: p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

-(+2/p)-5p+550=0

We add all the numbers together, and all the variables

-5p-(+2/p)+550=0

We get rid of parentheses

-5p-2/p+550=0

We multiply all the terms by the denominator


-5p*p+550*p-2=0

We add all the numbers together, and all the variables

550p-5p*p-2=0

Wy multiply elements

-5p^2+550p-2=0

a = -5; b = 550; c = -2;
Δ = b2-4ac
Δ = 5502-4·(-5)·(-2)
Δ = 302460
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:

$\sqrt{\Delta}=\sqrt{302460}=\sqrt{20164*15}=\sqrt{20164}*\sqrt{15}=142\sqrt{15}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(550)-142\sqrt{15}}{2*-5}=\frac{-550-142\sqrt{15}}{-10}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(550)+142\sqrt{15}}{2*-5}=\frac{-550+142\sqrt{15}}{-10}
$