2(2x-6)x+3=0

Solution for 2(2x-6)x+3=0 equation:

2(2x-6)x+3=0

We multiply parentheses

4x^2-12x+3=0

a = 4; b = -12; c = +3;
Δ = b2-4ac
Δ = -122-4·4·3
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{6}}{2*4}=\frac{12-4\sqrt{6}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{6}}{2*4}=\frac{12+4\sqrt{6}}{8}
$