3p-3/3p+2=5

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

3p-3/3p+2=5

We move all terms to the left:

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


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R


We add all the numbers together, and all the variables

3p-3/3p-3=0

We multiply all the terms by the denominator


3p*3p-3*3p-3=0

Wy multiply elements

9p^2-9p-3=0

a = 9; b = -9; c = -3;
Δ = b2-4ac
Δ = -92-4·9·(-3)
Δ = 189
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:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{21}}{2*9}=\frac{9-3\sqrt{21}}{18}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{21}}{2*9}=\frac{9+3\sqrt{21}}{18}
$