x(x-4*3^1/2)=-6

Solution for x(x-4*3^1/2)=-6 equation:

x(x-4*3^1/2)=-6

We move all terms to the left:

x(x-4*3^1/2)-(-6)=0

We add all the numbers together, and all the variables

x(x-4*3^1/2)+6=0

We multiply parentheses

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

We add all the numbers together, and all the variables

-11x^2+6=0

a = -11; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-11)·6
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{66}}{2*-11}=\frac{0-2\sqrt{66}}{-22}
=-\frac{2\sqrt{66}}{-22}
=-\frac{\sqrt{66}}{-11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{66}}{2*-11}=\frac{0+2\sqrt{66}}{-22}
=\frac{2\sqrt{66}}{-22}
=\frac{\sqrt{66}}{-11}
$