Solving quadratic equations by completing the square

Firstly, I just want to say I am NOT trying to cheat on homework or anything - this is one of many exercises in my textbook and I could easily copy from the answers if I wanted to, but I want to thoroughly understand it.

3x^2+12x-5=0
The answer I got was (+-√16/9)/2 but that was not the correct answer. The actual answer was (-6+-√51)/3.

So (if you can even understand me...) could someone please explain to me how to do questions like this, step by step? Thank you, answers much appreciated.

3x² + 12x - 5 = 0
3 (x² + 4x) = 5

Take half coefficient of x (4/2 = 2) and square it 2² = 4
Add this value inside bracket.
Don't forget to add same value to right side

3 (x² + 4x + 4) = 5 + 3(4)
3 (x + 2)² = 17 . . . . . . . . . multiply both sides by 3
9 (x + 2)² = 51
3 (x + 2) = ± √51
x + 2 = ± √51 / 3
x = -2 ± √51 / 3
x = (-6 ± √51) / 3

Ματπmφm

Step1:make the coefficient of x^2 as 1
so divide the equation by 3
=>x^2+4x-5/3=0
step2:now express the x coefficient as 2(any no)x
=>x^2+2(2)x-5/3=0
step3:now add and subtract the (any no)^2 to the equation
=>x^2+2(2)x+2^2-2^2-5/3=0
=>(x+2)^2-(4+5/3)=0
=>(x+2)^2=17/3
=>x+2=+-root(17/3)
=>x=-2+root(17/3) or x=-2-root(17/3)
hope you understood
on taking lcm with 3(root(17/3)=root(51)/3) we get
x=(-6-root(51))/3 or
x=(-6+root(51))/3

3x² + 12x - 5 = 0
x² + 2x = 5/3 + 2²
x² + 2x = 5/3 + 4
(x + 2)² = (5 + 12)/3
x + 2 = ± (√17/3) OR ± 2.38047614284

Answer: x = - 2 ± √(17/3) OR x = - 4.38047614284, 0.38047614284

Check:
3(- 4.38047614284)² + 12(- 4.38047614284) = 5
3(19.1885712379) - 52.565713714 = 5
57.565713714 - 52.565713714 = 5
5 = 5

3(0.38047614284) + 12(0.38047614284) = 5
3(0.14476209527) + 4.565713714 = 5
0.434286286 + 4.565713714 = 5
5 = 5

Divide both sides to 3;