2x+1/6x=-3

Solution for 2x+1/6x=-3 equation:

2x+1/6x=-3

We move all terms to the left:

2x+1/6x-(-3)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

2x+1/6x+3=0

We multiply all the terms by the denominator


2x*6x+3*6x+1=0

Wy multiply elements

12x^2+18x+1=0

a = 12; b = 18; c = +1;
Δ = b2-4ac
Δ = 182-4·12·1
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{69}}{2*12}=\frac{-18-2\sqrt{69}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{69}}{2*12}=\frac{-18+2\sqrt{69}}{24}
$