(3/5)p=3/10

Solution for (3/5)p=3/10 equation:

(3/5)p=3/10

We move all terms to the left:

(3/5)p-(3/10)=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

(+3/5)p-(+3/10)=0

We multiply parentheses

3p^2-(+3/10)=0

We get rid of parentheses

3p^2-3/10=0

We multiply all the terms by the denominator


3p^2*10-3=0

Wy multiply elements

30p^2-3=0

a = 30; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·30·(-3)
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{10}}{2*30}=\frac{0-6\sqrt{10}}{60}
=-\frac{6\sqrt{10}}{60}
=-\frac{\sqrt{10}}{10}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{10}}{2*30}=\frac{0+6\sqrt{10}}{60}
=\frac{6\sqrt{10}}{60}
=\frac{\sqrt{10}}{10}
$