Question

How do you solve `6x^2 - x -3 =0`?

Answer 1

`x~~ -0.63 , color(white)(xx) x~~0.79`

Explanation:

It is a matter of practice so that you get used to spotting the factors.

The only 2 factors you are going to get for 3 is 1 and 3. This is because 3 is a prime number. The thing is that we have -3 so one has to be positive and the other negative.
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Factors of 3 are only {1,3} because 3 is a prime number

Factors of 6 are {1,6} , {2,3}

Looking for -1 in `-x`

These factors do not work so revert to the standard solution formula:

`ax^2+bx+c=0`

where
`x=(-b+-sqrt(b^2-4ac))/(2a)`

`a=6`
`b=-1`
`c=-3`

`x=(-(-1)+-sqrt((-1)^2-4(6)(-3)))/(2(6))`

`color(green)("The use of brackets round negative numbers reduce")`
`color(green)("the chance of making a mistake!")`

`x=(1+-sqrt(1+72))/12`

`x=1/12 +- sqrt(73)/12`

`x~~0.08dot3 +-0.71`

`x~~ -0.63 , x~~0.79`