-1/6x-(x-3)=-36

Solution for -1/6x-(x-3)=-36 equation:

-1/6x-(x-3)=-36

We move all terms to the left:

-1/6x-(x-3)-(-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

-1/6x-(x-3)+36=0

We get rid of parentheses

-1/6x-x+3+36=0

We multiply all the terms by the denominator


-x*6x+3*6x+36*6x-1=0

Wy multiply elements

-6x^2+18x+216x-1=0

We add all the numbers together, and all the variables

-6x^2+234x-1=0

a = -6; b = 234; c = -1;
Δ = b2-4ac
Δ = 2342-4·(-6)·(-1)
Δ = 54732
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:

$\sqrt{\Delta}=\sqrt{54732}=\sqrt{4*13683}=\sqrt{4}*\sqrt{13683}=2\sqrt{13683}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(234)-2\sqrt{13683}}{2*-6}=\frac{-234-2\sqrt{13683}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(234)+2\sqrt{13683}}{2*-6}=\frac{-234+2\sqrt{13683}}{-12}
$