3x-6x^2=1/6

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

3x-6x^2=1/6

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-36x^2+18x-1=0

a = -36; b = 18; c = -1;
Δ = b2-4ac
Δ = 182-4·(-36)·(-1)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{5}}{2*-36}=\frac{-18-6\sqrt{5}}{-72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{5}}{2*-36}=\frac{-18+6\sqrt{5}}{-72}
$