72/2p=3p

Solution for 72/2p=3p equation:

72/2p=3p

We move all terms to the left:

72/2p-(3p)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R


We add all the numbers together, and all the variables

-3p+72/2p=0

We multiply all the terms by the denominator


-3p*2p+72=0

Wy multiply elements

-6p^2+72=0

a = -6; b = 0; c = +72;
Δ = b2-4ac
Δ = 02-4·(-6)·72
Δ = 1728
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:

$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{3}}{2*-6}=\frac{0-24\sqrt{3}}{-12}
=-\frac{24\sqrt{3}}{-12}
=-\frac{2\sqrt{3}}{-1}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{3}}{2*-6}=\frac{0+24\sqrt{3}}{-12}
=\frac{24\sqrt{3}}{-12}
=\frac{2\sqrt{3}}{-1}
$