0=6x^2-16x+9

Solution for 0=6x^2-16x+9 equation:

0=6x^2-16x+9

We move all terms to the left:

0-(6x^2-16x+9)=0

We add all the numbers together, and all the variables

-(6x^2-16x+9)=0

We get rid of parentheses

-6x^2+16x-9=0

a = -6; b = 16; c = -9;
Δ = b2-4ac
Δ = 162-4·(-6)·(-9)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{10}}{2*-6}=\frac{-16-2\sqrt{10}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{10}}{2*-6}=\frac{-16+2\sqrt{10}}{-12}
$