x^2-4x+11/3=0

Solution for x^2-4x+11/3=0 equation:

x^2-4x+11/3=0

We multiply all the terms by the denominator


x^2*3-4x*3+11=0

Wy multiply elements

3x^2-12x+11=0

a = 3; b = -12; c = +11;
Δ = b2-4ac
Δ = -122-4·3·11
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{3}}{2*3}=\frac{12-2\sqrt{3}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{3}}{2*3}=\frac{12+2\sqrt{3}}{6}
$