Question

How do you solve `21n ^ { 2} + 5n - 6= 0`?

Answer 1

`n=3/7, -2/3`

Explanation:

Given:
`color(white)(xxx)21n^2+5n-6=0`

`rArr 21n^2-9n+14n-6=0` [Broke up `5n` as `-9n +14n`]

`rArr 3n(7n-3)+2(7n-3)=0` [Grouping the Like Terms]

`rArr (7n - 3)(3n + 2)=0` [Group Again]

Now, If :

`3n+2=0`, then `3n=-2 rArr n= -2/3`

And If :

`7n-3=0`, then `7n=3 rArr n = 3/7`

Hence Explained.

Answer 2

`n=-2/3" or "n=3/7`

Explanation:

`"factorise the quadratic using the a-c method"`

`"that is factors of "21xx-6=-126" which sum to "+5`

`"the factors of "-126" which sum to + 5 are + 14 and - 9"`

`color(blue)"split the middle term using these factors"`

`rArr21n^2+14n-9n-6=0larrcolor(blue)"factor by grouping"`

`rArrcolor(red)(7n)(3n+2)color(red)(-3)(3n+2)=0`

`"take out the common factor "(3n+2)`

`rArr(3n+2)(color(red)(7n-3))=0`

`"equate each factor to zero and solve for n"`

`3n+2=0rArrn=-2/3`

`7n-3=0rArrn=3/7`