20+6/x=x

Solution for 20+6/x=x equation:

20+6/x=x

We move all terms to the left:

20+6/x-(x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-1x+6/x+20=0

We multiply all the terms by the denominator


-1x*x+20*x+6=0

We add all the numbers together, and all the variables

20x-1x*x+6=0

Wy multiply elements

-1x^2+20x+6=0

a = -1; b = 20; c = +6;
Δ = b2-4ac
Δ = 202-4·(-1)·6
Δ = 424
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:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{106}}{2*-1}=\frac{-20-2\sqrt{106}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{106}}{2*-1}=\frac{-20+2\sqrt{106}}{-2}
$