3/2p+5/p=8

Solution for 3/2p+5/p=8 equation:

3/2p+5/p=8

We move all terms to the left:

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


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R



Domain of the equation: p!=0

p∈R


We calculate fractions


3p/2p^2+10p/2p^2-8=0

We multiply all the terms by the denominator


3p+10p-8*2p^2=0

We add all the numbers together, and all the variables

13p-8*2p^2=0

Wy multiply elements

-16p^2+13p=0

a = -16; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-16)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-16}=\frac{-26}{-32}
=13/16
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-16}=\frac{0}{-32}
=0
$