3/2p=p+27

Solution for 3/2p=p+27 equation:

3/2p=p+27

We move all terms to the left:

3/2p-(p+27)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R


We get rid of parentheses

3/2p-p-27=0

We multiply all the terms by the denominator


-p*2p-27*2p+3=0

Wy multiply elements

-2p^2-54p+3=0

a = -2; b = -54; c = +3;
Δ = b2-4ac
Δ = -542-4·(-2)·3
Δ = 2940
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:

$\sqrt{\Delta}=\sqrt{2940}=\sqrt{196*15}=\sqrt{196}*\sqrt{15}=14\sqrt{15}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-14\sqrt{15}}{2*-2}=\frac{54-14\sqrt{15}}{-4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+14\sqrt{15}}{2*-2}=\frac{54+14\sqrt{15}}{-4}
$