9/6p=4/p+1

Solution for 9/6p=4/p+1 equation:

9/6p=4/p+1

We move all terms to the left:

9/6p-(4/p+1)=0


Domain of the equation: 6p!=0

p!=0/6

p!=0

p∈R



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

p∈R


We get rid of parentheses

9/6p-4/p-1=0

We calculate fractions


9p/6p^2+(-24p)/6p^2-1=0

We multiply all the terms by the denominator


9p+(-24p)-1*6p^2=0

Wy multiply elements

-6p^2+9p+(-24p)=0

We get rid of parentheses

-6p^2+9p-24p=0

We add all the numbers together, and all the variables

-6p^2-15p=0

a = -6; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·(-6)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*-6}=\frac{0}{-12}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*-6}=\frac{30}{-12}
=-2+1/2
$