2/3p-8=-4p+2+7

Solution for 2/3p-8=-4p+2+7 equation:

2/3p-8=-4p+2+7

We move all terms to the left:

2/3p-8-(-4p+2+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-(-4p+9)-8=0

We get rid of parentheses

2/3p+4p-9-8=0

We multiply all the terms by the denominator


4p*3p-9*3p-8*3p+2=0

Wy multiply elements

12p^2-27p-24p+2=0

We add all the numbers together, and all the variables

12p^2-51p+2=0

a = 12; b = -51; c = +2;
Δ = b2-4ac
Δ = -512-4·12·2
Δ = 2505
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-\sqrt{2505}}{2*12}=\frac{51-\sqrt{2505}}{24}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+\sqrt{2505}}{2*12}=\frac{51+\sqrt{2505}}{24}
$