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

2 Answers

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.

Mar 28, 2018

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