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

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

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

We move all terms to the left:

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


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

p∈R


We add all the numbers together, and all the variables

13p-(2/3p+5)=0

We get rid of parentheses

13p-2/3p-5=0

We multiply all the terms by the denominator


13p*3p-5*3p-2=0

Wy multiply elements

39p^2-15p-2=0

a = 39; b = -15; c = -2;
Δ = b2-4ac
Δ = -152-4·39·(-2)
Δ = 537
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{537}}{2*39}=\frac{15-\sqrt{537}}{78}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{537}}{2*39}=\frac{15+\sqrt{537}}{78}
$