6x-36x/6x-1=-36

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

6x-36x/6x-1=-36

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

6x-36x/6x+35=0

We multiply all the terms by the denominator


6x*6x-36x+35*6x=0

We add all the numbers together, and all the variables

-36x+6x*6x+35*6x=0

Wy multiply elements

36x^2-36x+210x=0

We add all the numbers together, and all the variables

36x^2+174x=0

a = 36; b = 174; c = 0;
Δ = b2-4ac
Δ = 1742-4·36·0
Δ = 30276
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{30276}=174$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(174)-174}{2*36}=\frac{-348}{72}
=-4+5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(174)+174}{2*36}=\frac{0}{72}
=0
$