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

Solution for x^2+x(1/6)-1/3=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

x^2+x^2-1/3=0

We multiply all the terms by the denominator


x^2*3+x^2*3-1=0

Wy multiply elements

3x^2+3x^2-1=0

We add all the numbers together, and all the variables

6x^2-1=0

a = 6; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·6·(-1)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{6}}{2*6}=\frac{0-2\sqrt{6}}{12}
=-\frac{2\sqrt{6}}{12}
=-\frac{\sqrt{6}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{6}}{2*6}=\frac{0+2\sqrt{6}}{12}
=\frac{2\sqrt{6}}{12}
=\frac{\sqrt{6}}{6}
$