2p=2/3p+6

Solution for 2p=2/3p+6 equation:

2p=2/3p+6

We move all terms to the left:

2p-(2/3p+6)=0


Domain of the equation: 3p+6)!=0

p∈R


We get rid of parentheses

2p-2/3p-6=0

We multiply all the terms by the denominator


2p*3p-6*3p-2=0

Wy multiply elements

6p^2-18p-2=0

a = 6; b = -18; c = -2;
Δ = b2-4ac
Δ = -182-4·6·(-2)
Δ = 372
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:

$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{93}}{2*6}=\frac{18-2\sqrt{93}}{12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{93}}{2*6}=\frac{18+2\sqrt{93}}{12}
$