(2/5)p=3/5

Solution for (2/5)p=3/5 equation:

(2/5)p=3/5

We move all terms to the left:

(2/5)p-(3/5)=0


Domain of the equation: 5)p!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

(+2/5)p-(+3/5)=0

We multiply parentheses

2p^2-(+3/5)=0

We get rid of parentheses

2p^2-3/5=0

We multiply all the terms by the denominator


2p^2*5-3=0

Wy multiply elements

10p^2-3=0

a = 10; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·10·(-3)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*10}=\frac{0-2\sqrt{30}}{20}
=-\frac{2\sqrt{30}}{20}
=-\frac{\sqrt{30}}{10}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*10}=\frac{0+2\sqrt{30}}{20}
=\frac{2\sqrt{30}}{20}
=\frac{\sqrt{30}}{10}
$