x^2+x/6=1

Solution for x^2+x/6=1 equation:

x^2+x/6=1

We move all terms to the left:

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

x^2*6+x-6=0

Wy multiply elements

6x^2+x-6=0

a = 6; b = 1; c = -6;
Δ = b2-4ac
Δ = 12-4·6·(-6)
Δ = 145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{145}}{2*6}=\frac{-1-\sqrt{145}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{145}}{2*6}=\frac{-1+\sqrt{145}}{12}
$