154/9p=p

Solution for 154/9p=p equation:

154/9p=p

We move all terms to the left:

154/9p-(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+154/9p=0

We multiply all the terms by the denominator


-1p*9p+154=0

Wy multiply elements

-9p^2+154=0

a = -9; b = 0; c = +154;
Δ = b2-4ac
Δ = 02-4·(-9)·154
Δ = 5544
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:

$\sqrt{\Delta}=\sqrt{5544}=\sqrt{36*154}=\sqrt{36}*\sqrt{154}=6\sqrt{154}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{154}}{2*-9}=\frac{0-6\sqrt{154}}{-18}
=-\frac{6\sqrt{154}}{-18}
=-\frac{\sqrt{154}}{-3}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{154}}{2*-9}=\frac{0+6\sqrt{154}}{-18}
=\frac{6\sqrt{154}}{-18}
=\frac{\sqrt{154}}{-3}
$