p=56/p+6

Solution for p=56/p+6 equation:

p=56/p+6

We move all terms to the left:

p-(56/p+6)=0


Domain of the equation: p+6)!=0

p∈R


We get rid of parentheses

p-56/p-6=0

We multiply all the terms by the denominator


p*p-6*p-56=0

We add all the numbers together, and all the variables

-6p+p*p-56=0

Wy multiply elements

p^2-6p-56=0

a = 1; b = -6; c = -56;
Δ = b2-4ac
Δ = -62-4·1·(-56)
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{65}}{2*1}=\frac{6-2\sqrt{65}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{65}}{2*1}=\frac{6+2\sqrt{65}}{2}
$