x^2/3-19x+39=0

Solution for x^2/3-19x+39=0 equation:

x^2/3-19x+39=0

We multiply all the terms by the denominator


x^2-19x*3+39*3=0

We add all the numbers together, and all the variables

x^2-19x*3+117=0

Wy multiply elements

x^2-57x+117=0

a = 1; b = -57; c = +117;
Δ = b2-4ac
Δ = -572-4·1·117
Δ = 2781
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:

$\sqrt{\Delta}=\sqrt{2781}=\sqrt{9*309}=\sqrt{9}*\sqrt{309}=3\sqrt{309}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-3\sqrt{309}}{2*1}=\frac{57-3\sqrt{309}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+3\sqrt{309}}{2*1}=\frac{57+3\sqrt{309}}{2}
$