X=20/p+6

Solution for X=20/p+6 equation:

X=20/X+6

We move all terms to the left:

X-(20/X+6)=0


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

X∈R


We get rid of parentheses

X-20/X-6=0

We multiply all the terms by the denominator


X*X-6*X-20=0

We add all the numbers together, and all the variables

-6X+X*X-20=0

Wy multiply elements

X^2-6X-20=0

a = 1; b = -6; c = -20;
Δ = b2-4ac
Δ = -62-4·1·(-20)
Δ = 116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{29}}{2*1}=\frac{6-2\sqrt{29}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{29}}{2*1}=\frac{6+2\sqrt{29}}{2}
$