15-3p=2/3p+5

Solution for 15-3p=2/3p+5 equation:

15-3p=2/3p+5

We move all terms to the left:

15-3p-(2/3p+5)=0


Domain of the equation: 3p+5)!=0

p∈R


We get rid of parentheses

-3p-2/3p-5+15=0

We multiply all the terms by the denominator


-3p*3p-5*3p+15*3p-2=0

Wy multiply elements

-9p^2-15p+45p-2=0

We add all the numbers together, and all the variables

-9p^2+30p-2=0

a = -9; b = 30; c = -2;
Δ = b2-4ac
Δ = 302-4·(-9)·(-2)
Δ = 828
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:

$\sqrt{\Delta}=\sqrt{828}=\sqrt{36*23}=\sqrt{36}*\sqrt{23}=6\sqrt{23}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{23}}{2*-9}=\frac{-30-6\sqrt{23}}{-18}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{23}}{2*-9}=\frac{-30+6\sqrt{23}}{-18}
$