X-1/6x=35

Solution for X-1/6x=35 equation:

X-1/6X=35

We move all terms to the left:

X-1/6X-(35)=0


Domain of the equation: 6X!=0

X!=0/6

X!=0

X∈R


We multiply all the terms by the denominator


X*6X-35*6X-1=0

Wy multiply elements

6X^2-210X-1=0

a = 6; b = -210; c = -1;
Δ = b2-4ac
Δ = -2102-4·6·(-1)
Δ = 44124
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:

$\sqrt{\Delta}=\sqrt{44124}=\sqrt{4*11031}=\sqrt{4}*\sqrt{11031}=2\sqrt{11031}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-210)-2\sqrt{11031}}{2*6}=\frac{210-2\sqrt{11031}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-210)+2\sqrt{11031}}{2*6}=\frac{210+2\sqrt{11031}}{12}
$