x(5/6)=1/3

Solution for x(5/6)=1/3 equation:

x(5/6)=1/3

We move all terms to the left:

x(5/6)-(1/3)=0

We add all the numbers together, and all the variables

x(+5/6)-(+1/3)=0

We multiply parentheses

5x^2-(+1/3)=0

We get rid of parentheses

5x^2-1/3=0

We multiply all the terms by the denominator


5x^2*3-1=0

Wy multiply elements

15x^2-1=0

a = 15; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·15·(-1)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{15}}{2*15}=\frac{0-2\sqrt{15}}{30}
=-\frac{2\sqrt{15}}{30}
=-\frac{\sqrt{15}}{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{15}}{2*15}=\frac{0+2\sqrt{15}}{30}
=\frac{2\sqrt{15}}{30}
=\frac{\sqrt{15}}{15}
$