1/3p-9/8p=3

Solution for 1/3p-9/8p=3 equation:

1/3p-9/8p=3

We move all terms to the left:

1/3p-9/8p-(3)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R



Domain of the equation: 8p!=0

p!=0/8

p!=0

p∈R


We calculate fractions


8p/24p^2+(-27p)/24p^2-3=0

We multiply all the terms by the denominator


8p+(-27p)-3*24p^2=0

Wy multiply elements

-72p^2+8p+(-27p)=0

We get rid of parentheses

-72p^2+8p-27p=0

We add all the numbers together, and all the variables

-72p^2-19p=0

a = -72; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·(-72)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*-72}=\frac{0}{-144}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*-72}=\frac{38}{-144}
=-19/72
$