2/3p-24=-2p

Solution for 2/3p-24=-2p equation:

2/3p-24=-2p

We move all terms to the left:

2/3p-24-(-2p)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R


We get rid of parentheses

2/3p+2p-24=0

We multiply all the terms by the denominator


2p*3p-24*3p+2=0

Wy multiply elements

6p^2-72p+2=0

a = 6; b = -72; c = +2;
Δ = b2-4ac
Δ = -722-4·6·2
Δ = 5136
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:

$\sqrt{\Delta}=\sqrt{5136}=\sqrt{16*321}=\sqrt{16}*\sqrt{321}=4\sqrt{321}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{321}}{2*6}=\frac{72-4\sqrt{321}}{12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{321}}{2*6}=\frac{72+4\sqrt{321}}{12}
$