3p+3=2/3p+5

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

3p+3=2/3p+5

We move all terms to the left:

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


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

p∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

9p^2-6p-2=0

a = 9; b = -6; c = -2;
Δ = b2-4ac
Δ = -62-4·9·(-2)
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{3}}{2*9}=\frac{6-6\sqrt{3}}{18}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{3}}{2*9}=\frac{6+6\sqrt{3}}{18}
$