1/6x-17=2x+5

Solution for 1/6x-17=2x+5 equation:

1/6x-17=2x+5

We move all terms to the left:

1/6x-17-(2x+5)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

1/6x-2x-5-17=0

We multiply all the terms by the denominator


-2x*6x-5*6x-17*6x+1=0

Wy multiply elements

-12x^2-30x-102x+1=0

We add all the numbers together, and all the variables

-12x^2-132x+1=0

a = -12; b = -132; c = +1;
Δ = b2-4ac
Δ = -1322-4·(-12)·1
Δ = 17472
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:

$\sqrt{\Delta}=\sqrt{17472}=\sqrt{64*273}=\sqrt{64}*\sqrt{273}=8\sqrt{273}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-132)-8\sqrt{273}}{2*-12}=\frac{132-8\sqrt{273}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+8\sqrt{273}}{2*-12}=\frac{132+8\sqrt{273}}{-24}
$