x-1/6x=120

Solution for x-1/6x=120 equation:

x-1/6x=120

We move all terms to the left:

x-1/6x-(120)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

6x^2-720x-1=0

a = 6; b = -720; c = -1;
Δ = b2-4ac
Δ = -7202-4·6·(-1)
Δ = 518424
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:

$\sqrt{\Delta}=\sqrt{518424}=\sqrt{4*129606}=\sqrt{4}*\sqrt{129606}=2\sqrt{129606}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-720)-2\sqrt{129606}}{2*6}=\frac{720-2\sqrt{129606}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-720)+2\sqrt{129606}}{2*6}=\frac{720+2\sqrt{129606}}{12}
$