3/4p+6=1/9p

Solution for 3/4p+6=1/9p equation:

3/4p+6=1/9p

We move all terms to the left:

3/4p+6-(1/9p)=0


Domain of the equation: 4p!=0

p!=0/4

p!=0

p∈R



Domain of the equation: 9p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

3/4p-(+1/9p)+6=0

We get rid of parentheses

3/4p-1/9p+6=0

We calculate fractions


27p/36p^2+(-4p)/36p^2+6=0

We multiply all the terms by the denominator


27p+(-4p)+6*36p^2=0

Wy multiply elements

216p^2+27p+(-4p)=0

We get rid of parentheses

216p^2+27p-4p=0

We add all the numbers together, and all the variables

216p^2+23p=0

a = 216; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·216·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*216}=\frac{-46}{432}
=-23/216
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*216}=\frac{0}{432}
=0
$