3x^2+x-(1/12)=0

Solution for 3x^2+x-(1/12)=0 equation:

3x^2+x-(1/12)=0

We add all the numbers together, and all the variables

3x^2+x-(+1/12)=0

We get rid of parentheses

3x^2+x-1/12=0

We multiply all the terms by the denominator


3x^2*12+x*12-1=0

Wy multiply elements

36x^2+12x-1=0

a = 36; b = 12; c = -1;
Δ = b2-4ac
Δ = 122-4·36·(-1)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{2}}{2*36}=\frac{-12-12\sqrt{2}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{2}}{2*36}=\frac{-12+12\sqrt{2}}{72}
$