1/5p=22;p=

Solution for 1/5p=22;p= equation:

1/5p=22p=

We move all terms to the left:

1/5p-(22p)=0


Domain of the equation: 5p!=0

p!=0/5

p!=0

p∈R


We add all the numbers together, and all the variables

-22p+1/5p=0

We multiply all the terms by the denominator


-22p*5p+1=0

Wy multiply elements

-110p^2+1=0

a = -110; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-110)·1
Δ = 440
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:

$\sqrt{\Delta}=\sqrt{440}=\sqrt{4*110}=\sqrt{4}*\sqrt{110}=2\sqrt{110}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{110}}{2*-110}=\frac{0-2\sqrt{110}}{-220}
=-\frac{2\sqrt{110}}{-220}
=-\frac{\sqrt{110}}{-110}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{110}}{2*-110}=\frac{0+2\sqrt{110}}{-220}
=\frac{2\sqrt{110}}{-220}
=\frac{\sqrt{110}}{-110}
$