16-3p=2/3p+3

Solution for 16-3p=2/3p+3 equation:

16-3p=2/3p+3

We move all terms to the left:

16-3p-(2/3p+3)=0


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

p∈R


We get rid of parentheses

-3p-2/3p-3+16=0

We multiply all the terms by the denominator


-3p*3p-3*3p+16*3p-2=0

Wy multiply elements

-9p^2-9p+48p-2=0

We add all the numbers together, and all the variables

-9p^2+39p-2=0

a = -9; b = 39; c = -2;
Δ = b2-4ac
Δ = 392-4·(-9)·(-2)
Δ = 1449
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:

$\sqrt{\Delta}=\sqrt{1449}=\sqrt{9*161}=\sqrt{9}*\sqrt{161}=3\sqrt{161}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-3\sqrt{161}}{2*-9}=\frac{-39-3\sqrt{161}}{-18}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+3\sqrt{161}}{2*-9}=\frac{-39+3\sqrt{161}}{-18}
$