4/9p+72=p

Solution for 4/9p+72=p equation:

4/9p+72=p

We move all terms to the left:

4/9p+72-(p)=0


Domain of the equation: 9p!=0

p!=0/9

p!=0

p∈R


We add all the numbers together, and all the variables

-1p+4/9p+72=0

We multiply all the terms by the denominator


-1p*9p+72*9p+4=0

Wy multiply elements

-9p^2+648p+4=0

a = -9; b = 648; c = +4;
Δ = b2-4ac
Δ = 6482-4·(-9)·4
Δ = 420048
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{420048}=\sqrt{144*2917}=\sqrt{144}*\sqrt{2917}=12\sqrt{2917}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(648)-12\sqrt{2917}}{2*-9}=\frac{-648-12\sqrt{2917}}{-18}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(648)+12\sqrt{2917}}{2*-9}=\frac{-648+12\sqrt{2917}}{-18}
$