6x=(-1/3)

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Solution for 6x=(-1/3) equation:



6x=(-1/3)
We move all terms to the left:
6x-((-1/3))=0
We multiply all the terms by the denominator
6x*3))-((-1=0
Wy multiply elements
18x^2-1=0
a = 18; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·18·(-1)
Δ = 72
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:
$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{2}}{2*18}=\frac{0-6\sqrt{2}}{36} =-\frac{6\sqrt{2}}{36} =-\frac{\sqrt{2}}{6} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{2}}{2*18}=\frac{0+6\sqrt{2}}{36} =\frac{6\sqrt{2}}{36} =\frac{\sqrt{2}}{6} $

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