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

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

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

We add all the numbers together, and all the variables

-1x^2+4x-8/3=0

We multiply all the terms by the denominator


-1x^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}
$