p-5/p=1=2/3

Solution for p-5/p=1=2/3 equation:

p-5/p=1=2/3

We move all terms to the left:

p-5/p-(1)=0


Domain of the equation: p!=0

p∈R


We multiply all the terms by the denominator


p*p-1*p-5=0

We add all the numbers together, and all the variables

-1p+p*p-5=0

Wy multiply elements

p^2-1p-5=0

a = 1; b = -1; c = -5;
Δ = b2-4ac
Δ = -12-4·1·(-5)
Δ = 21
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{21}}{2*1}=\frac{1-\sqrt{21}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{21}}{2*1}=\frac{1+\sqrt{21}}{2}
$