0=6x^2-16x+4

Solution for 0=6x^2-16x+4 equation:

0=6x^2-16x+4

We move all terms to the left:

0-(6x^2-16x+4)=0

We add all the numbers together, and all the variables

-(6x^2-16x+4)=0

We get rid of parentheses

-6x^2+16x-4=0

a = -6; b = 16; c = -4;
Δ = b2-4ac
Δ = 162-4·(-6)·(-4)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{10}}{2*-6}=\frac{-16-4\sqrt{10}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{10}}{2*-6}=\frac{-16+4\sqrt{10}}{-12}
$