1/6x-1=36x

Solution for 1/6x-1=36x equation:

1/6x-1=36x

We move all terms to the left:

1/6x-1-(36x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

-36x+1/6x-1=0

We multiply all the terms by the denominator


-36x*6x-1*6x+1=0

Wy multiply elements

-216x^2-6x+1=0

a = -216; b = -6; c = +1;
Δ = b2-4ac
Δ = -62-4·(-216)·1
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-30}{2*-216}=\frac{-24}{-432}
=1/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+30}{2*-216}=\frac{36}{-432}
=-1/12
$