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

16.3p-2/3p-5=0

We multiply all the terms by the denominator


(16.3p)*3p-5*3p-2=0

We add all the numbers together, and all the variables

(+16.3p)*3p-5*3p-2=0

We multiply parentheses

48p^2-5*3p-2=0

Wy multiply elements

48p^2-15p-2=0

a = 48; b = -15; c = -2;
Δ = b2-4ac
Δ = -152-4·48·(-2)
Δ = 609
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{609}}{2*48}=\frac{15-\sqrt{609}}{96}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{609}}{2*48}=\frac{15+\sqrt{609}}{96}
$