16-3p=2/3p-5

Solution for 16-3p=2/3p-5 equation:

16-3p=2/3p-5

We move all terms to the left:

16-3p-(2/3p-5)=0


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

p∈R


We get rid of parentheses

-3p-2/3p+5+16=0

We multiply all the terms by the denominator


-3p*3p+5*3p+16*3p-2=0

Wy multiply elements

-9p^2+15p+48p-2=0

We add all the numbers together, and all the variables

-9p^2+63p-2=0

a = -9; b = 63; c = -2;
Δ = b2-4ac
Δ = 632-4·(-9)·(-2)
Δ = 3897
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:

$\sqrt{\Delta}=\sqrt{3897}=\sqrt{9*433}=\sqrt{9}*\sqrt{433}=3\sqrt{433}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-3\sqrt{433}}{2*-9}=\frac{-63-3\sqrt{433}}{-18}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+3\sqrt{433}}{2*-9}=\frac{-63+3\sqrt{433}}{-18}
$