3/5p=32+p

Solution for 3/5p=32+p equation:

3/5p=32+p

We move all terms to the left:

3/5p-(32+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

3/5p-(p+32)=0

We get rid of parentheses

3/5p-p-32=0

We multiply all the terms by the denominator


-p*5p-32*5p+3=0

Wy multiply elements

-5p^2-160p+3=0

a = -5; b = -160; c = +3;
Δ = b2-4ac
Δ = -1602-4·(-5)·3
Δ = 25660
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:

$\sqrt{\Delta}=\sqrt{25660}=\sqrt{4*6415}=\sqrt{4}*\sqrt{6415}=2\sqrt{6415}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-2\sqrt{6415}}{2*-5}=\frac{160-2\sqrt{6415}}{-10}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+2\sqrt{6415}}{2*-5}=\frac{160+2\sqrt{6415}}{-10}
$