x^2-4x+8/3=0

Solution for x^2-4x+8/3=0 equation:

x^2-4x+8/3=0

We multiply all the terms by the denominator


x^2*3-4x*3+8=0

Wy multiply elements

3x^2-12x+8=0

a = 3; b = -12; c = +8;
Δ = b2-4ac
Δ = -122-4·3·8
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{3}}{2*3}=\frac{12-4\sqrt{3}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{3}}{2*3}=\frac{12+4\sqrt{3}}{6}
$