3/2p+3/2+4/3p=-11/4

Solution for 3/2p+3/2+4/3p=-11/4 equation:

3/2p+3/2+4/3p=-11/4

We move all terms to the left:

3/2p+3/2+4/3p-(-11/4)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R



Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R


We get rid of parentheses

3/2p+4/3p+3/2+11/4=0

We calculate fractions


396p^2/96p^2+144p/96p^2+128p/96p^2+144p/96p^2=0

We multiply all the terms by the denominator


396p^2+144p+128p+144p=0

We add all the numbers together, and all the variables

396p^2+416p=0

a = 396; b = 416; c = 0;
Δ = b2-4ac
Δ = 4162-4·396·0
Δ = 173056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{173056}=416$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(416)-416}{2*396}=\frac{-832}{792}
=-1+5/99
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(416)+416}{2*396}=\frac{0}{792}
=0
$