(5p+2)-(16/3p+1)=8

Solution for (5p+2)-(16/3p+1)=8 equation:

(5p+2)-(16/3p+1)=8

We move all terms to the left:

(5p+2)-(16/3p+1)-(8)=0


Domain of the equation: 3p+1)!=0

p∈R


We get rid of parentheses

5p-16/3p+2-1-8=0

We multiply all the terms by the denominator


5p*3p+2*3p-1*3p-8*3p-16=0

Wy multiply elements

15p^2+6p-3p-24p-16=0

We add all the numbers together, and all the variables

15p^2-21p-16=0

a = 15; b = -21; c = -16;
Δ = b2-4ac
Δ = -212-4·15·(-16)
Δ = 1401
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{-(-21)-\sqrt{1401}}{2*15}=\frac{21-\sqrt{1401}}{30}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{1401}}{2*15}=\frac{21+\sqrt{1401}}{30}
$