p=4/p+9=

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

p=4/p+9=

We move all terms to the left:

p-(4/p+9)=0


Domain of the equation: p+9)!=0

p∈R


We get rid of parentheses

p-4/p-9=0

We multiply all the terms by the denominator


p*p-9*p-4=0

We add all the numbers together, and all the variables

-9p+p*p-4=0

Wy multiply elements

p^2-9p-4=0

a = 1; b = -9; c = -4;
Δ = b2-4ac
Δ = -92-4·1·(-4)
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{97}}{2*1}=\frac{9-\sqrt{97}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{97}}{2*1}=\frac{9+\sqrt{97}}{2}
$