6x2+x-1/3=0

Solution for 6x2+x-1/3=0 equation:

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

We multiply all the terms by the denominator


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

Wy multiply elements

18x^2+3x-1=0

a = 18; b = 3; c = -1;
Δ = b2-4ac
Δ = 32-4·18·(-1)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-9}{2*18}=\frac{-12}{36}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+9}{2*18}=\frac{6}{36}
=1/6
$