0=9x-3+6x^2

Solution for 0=9x-3+6x^2 equation:

0=9x-3+6x^2

We move all terms to the left:

0-(9x-3+6x^2)=0

We add all the numbers together, and all the variables

-(9x-3+6x^2)=0

We get rid of parentheses

-6x^2-9x+3=0

a = -6; b = -9; c = +3;
Δ = b2-4ac
Δ = -92-4·(-6)·3
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{17}}{2*-6}=\frac{9-3\sqrt{17}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{17}}{2*-6}=\frac{9+3\sqrt{17}}{-12}
$