Can any of you nice folks explain factoring and quadratic formula to me

Equation is 10x^2 -7x + 1 = 0

x = ______ or _________

you have to factor and use quadratic formula, I'm so confused and would appreciate it very much if somebody can do this one problem for me so I can understand it.

10x^2 - 7x + 1 = 0

(-5x + 1)(-2x + 1) = 0

x = 1/5
x = 1/2


(7 ± √9) / 20
(7 ± 3) / 20

x = 4/20
x = 1/5

x = 10/20
x = 1/2

x=3/5
x=-1
all i did was switch the one to the other side which makes it negative one then take an x out of ten x square minus seven x which looks like this x(10x -7) then use the inside and solve for x so u place 7 on the other side which turns positive and adds to negative one then solve and u get 3/5 after that the x= -1
i am not 100 percent sure i would check it on a graphing calculator but im pretty sure thats how you do it

Here S = sum of two numbers = -7
and P = product = 10*1 = 10
Brake -7 in to two pars such that their product is equal to 10
10x^2 -5x -2x +1 =0
5x(2x-1) -1(2x-1) =0
(5x-1)(2x-1) = 0
x = 1/5 or 1/2 ...............Ans

You dont need to factor because its in quadratic form.

So just plug in values a, b and c...

Its really easy, you are just over complicating it.