4/9p+9=1/2p

Solution for 4/9p+9=1/2p equation:

4/9p+9=1/2p

We move all terms to the left:

4/9p+9-(1/2p)=0


Domain of the equation: 9p!=0

p!=0/9

p!=0

p∈R



Domain of the equation: 2p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

4/9p-(+1/2p)+9=0

We get rid of parentheses

4/9p-1/2p+9=0

We calculate fractions


8p/18p^2+(-9p)/18p^2+9=0

We multiply all the terms by the denominator


8p+(-9p)+9*18p^2=0

Wy multiply elements

162p^2+8p+(-9p)=0

We get rid of parentheses

162p^2+8p-9p=0

We add all the numbers together, and all the variables

162p^2-1p=0

a = 162; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·162·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*162}=\frac{0}{324}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*162}=\frac{2}{324}
=1/162
$