x^2/2-6x+12=0

Solution for x^2/2-6x+12=0 equation:

x^2/2-6x+12=0

We multiply all the terms by the denominator


x^2-6x*2+12*2=0

We add all the numbers together, and all the variables

x^2-6x*2+24=0

Wy multiply elements

x^2-12x+24=0

a = 1; b = -12; c = +24;
Δ = b2-4ac
Δ = -122-4·1·24
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*1}=\frac{12-4\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{3}}{2*1}=\frac{12+4\sqrt{3}}{2}
$