Help me solve -6x² +5x -1 = 0?

-1*(6x² -5x +1) = 0

6x² -5x +1=0

(3x-1)(2x-1)=0

3x-1=0 then x=1/3
2x-1=0 then x=1/2

so x is 1/3 and 1/2

- 6x² + 5x - 1 = 0
6x² - 5x = - 1
x² - 5/6x = - 1/6
x² - 5/12x = - 1/6 + (- 5/12)²
x² - 5/12x = - 24/144 + 25/144
(x - 5/12)² = 1/144
x - 5/12 = 1/12

x = 1/12 + 5/12, x = 6/12, x = 1/2
x = - 1/12 + 5/12, = x + 4/12, x = 1/3

Answer: x = 1/2, 1/3

Proof (x = 1/2):
- 6(1/2)² + 5(1/2) = 1
- 6(1/4) + 5/2 = 1
- 3/2 + 5/2 = 1
2/2 = 1
1 = 1

Proof (x = 1/3):
- 6(1/3)² + 5(1/3) = 1
- 6(1/9) + 5/3 = 1
- 2/3 + 5/3 = 1
3/3 = 1
1 = 1

6x² - 5x + 1 = 0
(6x + 1)(x - 1) = 0
x = - 1/6 , x = 1

(-3x+1) (2x-1)=0
x=1/3, 1/2

-6x^2 + 5x - 1 = 0
6x^2 - 5x + 1 = 0
6x^2 - 2x - 3x + 1 = 0
(6x^2 - 2x) - (3x - 1) = 0
2x(3x - 1) - 1(3x - 1) = 0
(3x - 1)(2x - 1) = 0

3x - 1 = 0
3x = 1
x = 1/3

2x - 1 = 0
2x = 1
x = 1/2 (0.5)

∴ x = 1/3 , 1/2 (0.5)

x = -b + or - root b^2 - 4ac/2a

x = -5 + or - root (36 - 24) / - 12

x = -5 + or - root 12 / -12

x = -5 + or - 3.46/-12

x = - 1.54/-12 = 0.13

OR x = -8.46/-12 = 0.71

-6x² +5x -1 = 0
there are basically two methods of solving:
METHOD 1 (Splitting the middle term)
find 2 no:s such that the sum is 5 and product is 6
-6x + 2x + 3x -1 = 0
-2x(-3x - 1) - 1(-3x - 1) = 0
(-3x - 1)(-2x -1) = 0
therefore (-3x - 1) = 0 and (-2x -1) = 0
therefore x = -1/3 and x = -1/2

METHOD 2 (Using quadratic formula)
x = [-b +or- square root of (b^2 - 4ac)]/2a
here, a = -6 b = 5 c = -1
substituting in the equation we get x = -1/3 and x = -1/2

6x² - 5x + 1 = 0
(3x - 1)(2x - 1) = 0
x = 1/3 or 1/2