-1/6x-x-3=-39

Solution for -1/6x-x-3=-39 equation:

-1/6x-x-3=-39

We move all terms to the left:

-1/6x-x-3-(-39)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -6; b = 216; c = -1;
Δ = b2-4ac
Δ = 2162-4·(-6)·(-1)
Δ = 46632
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:

$\sqrt{\Delta}=\sqrt{46632}=\sqrt{4*11658}=\sqrt{4}*\sqrt{11658}=2\sqrt{11658}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(216)-2\sqrt{11658}}{2*-6}=\frac{-216-2\sqrt{11658}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(216)+2\sqrt{11658}}{2*-6}=\frac{-216+2\sqrt{11658}}{-12}
$