120/x-6=x

Solution for 120/x-6=x equation:

120/x-6=x

We move all terms to the left:

120/x-6-(x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-1x+120/x-6=0

We multiply all the terms by the denominator


-1x*x-6*x+120=0

We add all the numbers together, and all the variables

-6x-1x*x+120=0

Wy multiply elements

-1x^2-6x+120=0

a = -1; b = -6; c = +120;
Δ = b2-4ac
Δ = -62-4·(-1)·120
Δ = 516
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:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{129}}{2*-1}=\frac{6-2\sqrt{129}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{129}}{2*-1}=\frac{6+2\sqrt{129}}{-2}
$