X-1/6x=26

Solution for X-1/6x=26 equation:

X-1/6X=26

We move all terms to the left:

X-1/6X-(26)=0


Domain of the equation: 6X!=0

X!=0/6

X!=0

X∈R


We multiply all the terms by the denominator


X*6X-26*6X-1=0

Wy multiply elements

6X^2-156X-1=0

a = 6; b = -156; c = -1;
Δ = b2-4ac
Δ = -1562-4·6·(-1)
Δ = 24360
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:

$\sqrt{\Delta}=\sqrt{24360}=\sqrt{4*6090}=\sqrt{4}*\sqrt{6090}=2\sqrt{6090}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-156)-2\sqrt{6090}}{2*6}=\frac{156-2\sqrt{6090}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-156)+2\sqrt{6090}}{2*6}=\frac{156+2\sqrt{6090}}{12}
$