2/3p-9=p+15

Solution for 2/3p-9=p+15 equation:

2/3p-9=p+15

We move all terms to the left:

2/3p-9-(p+15)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R


We get rid of parentheses

2/3p-p-15-9=0

We multiply all the terms by the denominator


-p*3p-15*3p-9*3p+2=0

Wy multiply elements

-3p^2-45p-27p+2=0

We add all the numbers together, and all the variables

-3p^2-72p+2=0

a = -3; b = -72; c = +2;
Δ = b2-4ac
Δ = -722-4·(-3)·2
Δ = 5208
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:

$\sqrt{\Delta}=\sqrt{5208}=\sqrt{4*1302}=\sqrt{4}*\sqrt{1302}=2\sqrt{1302}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-2\sqrt{1302}}{2*-3}=\frac{72-2\sqrt{1302}}{-6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+2\sqrt{1302}}{2*-3}=\frac{72+2\sqrt{1302}}{-6}
$