3/5p=32p

Solution for 3/5p=32p equation:

3/5p=32p

We move all terms to the left:

3/5p-(32p)=0


Domain of the equation: 5p!=0

p!=0/5

p!=0

p∈R


We add all the numbers together, and all the variables

-32p+3/5p=0

We multiply all the terms by the denominator


-32p*5p+3=0

Wy multiply elements

-160p^2+3=0

a = -160; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-160)·3
Δ = 1920
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:

$\sqrt{\Delta}=\sqrt{1920}=\sqrt{64*30}=\sqrt{64}*\sqrt{30}=8\sqrt{30}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{30}}{2*-160}=\frac{0-8\sqrt{30}}{-320}
=-\frac{8\sqrt{30}}{-320}
=-\frac{\sqrt{30}}{-40}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{30}}{2*-160}=\frac{0+8\sqrt{30}}{-320}
=\frac{8\sqrt{30}}{-320}
=\frac{\sqrt{30}}{-40}
$