1-1/6x=27+2x

Solution for 1-1/6x=27+2x equation:

1-1/6x=27+2x

We move all terms to the left:

1-1/6x-(27+2x)=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-(2x+27)+1=0

We get rid of parentheses

-1/6x-2x-27+1=0

We multiply all the terms by the denominator


-2x*6x-27*6x+1*6x-1=0

Wy multiply elements

-12x^2-162x+6x-1=0

We add all the numbers together, and all the variables

-12x^2-156x-1=0

a = -12; b = -156; c = -1;
Δ = b2-4ac
Δ = -1562-4·(-12)·(-1)
Δ = 24288
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:

$\sqrt{\Delta}=\sqrt{24288}=\sqrt{16*1518}=\sqrt{16}*\sqrt{1518}=4\sqrt{1518}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-156)-4\sqrt{1518}}{2*-12}=\frac{156-4\sqrt{1518}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-156)+4\sqrt{1518}}{2*-12}=\frac{156+4\sqrt{1518}}{-24}
$