x2/3+x1/3-6=0

Solution for x2/3+x1/3-6=0 equation:

x2/3+x1/3-6=0

We multiply all the terms by the denominator


x2+x1-6*3=0

We add all the numbers together, and all the variables

x^2+x-18=0

a = 1; b = 1; c = -18;
Δ = b2-4ac
Δ = 12-4·1·(-18)
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{73}}{2*1}=\frac{-1-\sqrt{73}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{73}}{2*1}=\frac{-1+\sqrt{73}}{2}
$