20p-(5/p)=21

Solution for 20p-(5/p)=21 equation:

20p-(5/p)=21

We move all terms to the left:

20p-(5/p)-(21)=0


Domain of the equation: p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

20p-(+5/p)-21=0

We get rid of parentheses

20p-5/p-21=0

We multiply all the terms by the denominator


20p*p-21*p-5=0

We add all the numbers together, and all the variables

-21p+20p*p-5=0

Wy multiply elements

20p^2-21p-5=0

a = 20; b = -21; c = -5;
Δ = b2-4ac
Δ = -212-4·20·(-5)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-29}{2*20}=\frac{-8}{40}
=-1/5
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+29}{2*20}=\frac{50}{40}
=1+1/4
$