20=p-4/p=16

Solution for 20=p-4/p=16 equation:

20=p-4/p=16

We move all terms to the left:

20-(p-4/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

-(+p-4/p)+20=0

We get rid of parentheses

-p+4/p+20=0

We multiply all the terms by the denominator


-p*p+20*p+4=0

We add all the numbers together, and all the variables

20p-p*p+4=0

Wy multiply elements

-1p^2+20p+4=0

a = -1; b = 20; c = +4;
Δ = b2-4ac
Δ = 202-4·(-1)·4
Δ = 416
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:

$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{26}}{2*-1}=\frac{-20-4\sqrt{26}}{-2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{26}}{2*-1}=\frac{-20+4\sqrt{26}}{-2}
$