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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

-9x^2+3x=0

a = -9; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-9)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-9}=\frac{-6}{-18}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-9}=\frac{0}{-18}
=0
$