32-3p=1/2p

Solution for 32-3p=1/2p equation:

32-3p=1/2p

We move all terms to the left:

32-3p-(1/2p)=0


Domain of the equation: 2p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

-3p-(+1/2p)+32=0

We get rid of parentheses

-3p-1/2p+32=0

We multiply all the terms by the denominator


-3p*2p+32*2p-1=0

Wy multiply elements

-6p^2+64p-1=0

a = -6; b = 64; c = -1;
Δ = b2-4ac
Δ = 642-4·(-6)·(-1)
Δ = 4072
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:

$\sqrt{\Delta}=\sqrt{4072}=\sqrt{4*1018}=\sqrt{4}*\sqrt{1018}=2\sqrt{1018}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-2\sqrt{1018}}{2*-6}=\frac{-64-2\sqrt{1018}}{-12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+2\sqrt{1018}}{2*-6}=\frac{-64+2\sqrt{1018}}{-12}
$