2/3p-24/3=-2p-1+7

Solution for 2/3p-24/3=-2p-1+7 equation:

2/3p-24/3=-2p-1+7

We move all terms to the left:

2/3p-24/3-(-2p-1+7)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R


We add all the numbers together, and all the variables

2/3p-(-2p+6)-24/3=0

We add all the numbers together, and all the variables

2/3p-(-2p+6)-8=0

We get rid of parentheses

2/3p+2p-6-8=0

We multiply all the terms by the denominator


2p*3p-6*3p-8*3p+2=0

Wy multiply elements

6p^2-18p-24p+2=0

We add all the numbers together, and all the variables

6p^2-42p+2=0

a = 6; b = -42; c = +2;
Δ = b2-4ac
Δ = -422-4·6·2
Δ = 1716
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:

$\sqrt{\Delta}=\sqrt{1716}=\sqrt{4*429}=\sqrt{4}*\sqrt{429}=2\sqrt{429}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{429}}{2*6}=\frac{42-2\sqrt{429}}{12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{429}}{2*6}=\frac{42+2\sqrt{429}}{12}
$