41/5p=p

Solution for 41/5p=p equation:

41/5p=p

We move all terms to the left:

41/5p-(p)=0


Domain of the equation: 5p!=0

p!=0/5

p!=0

p∈R


We add all the numbers together, and all the variables

-1p+41/5p=0

We multiply all the terms by the denominator


-1p*5p+41=0

Wy multiply elements

-5p^2+41=0

a = -5; b = 0; c = +41;
Δ = b2-4ac
Δ = 02-4·(-5)·41
Δ = 820
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:

$\sqrt{\Delta}=\sqrt{820}=\sqrt{4*205}=\sqrt{4}*\sqrt{205}=2\sqrt{205}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{205}}{2*-5}=\frac{0-2\sqrt{205}}{-10}
=-\frac{2\sqrt{205}}{-10}
=-\frac{\sqrt{205}}{-5}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{205}}{2*-5}=\frac{0+2\sqrt{205}}{-10}
=\frac{2\sqrt{205}}{-10}
=\frac{\sqrt{205}}{-5}
$