x-1/6x=105

Solution for x-1/6x=105 equation:

x-1/6x=105

We move all terms to the left:

x-1/6x-(105)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We multiply all the terms by the denominator


x*6x-105*6x-1=0

Wy multiply elements

6x^2-630x-1=0

a = 6; b = -630; c = -1;
Δ = b2-4ac
Δ = -6302-4·6·(-1)
Δ = 396924
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:

$\sqrt{\Delta}=\sqrt{396924}=\sqrt{4*99231}=\sqrt{4}*\sqrt{99231}=2\sqrt{99231}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-630)-2\sqrt{99231}}{2*6}=\frac{630-2\sqrt{99231}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-630)+2\sqrt{99231}}{2*6}=\frac{630+2\sqrt{99231}}{12}
$