Question

I need help. What does n equal.

`5n^(2)=7n-2`

Answer 1

• 
  `\pmb{ n= (2)/(5) \:or~ n=1}`

Explanation:

`\hookrightarrow\sf{5n^2 = 7n -2}\\\\\hookrightarrow\sf{5n^2 - 7n +2=0}\\\\\hookrightarrow\sf{5n^2 - (5+2)n +2=0}\\\\\hookrightarrow\sf{5n^2 - 5n -2n+2=0}\\\\\hookrightarrow\sf{ 5n(n - 1) -2(n-1)=0}\\\\\hookrightarrow\sf{ (5n-2)(n-1)=0}\\\\\hookrightarrow\sf{ 5n-2= 0\:or~ n-1=0}\\\\\hookrightarrow\sf{ 5n= 2\:or~n=1}\\\\\hookrightarrow\bold{ n= (2)/(5) \:or~ n=1}`

Answer 2

`\boxed{\sf n= (2)/(5) ,\: n=1}`

Explanation:

`\rightarrow 5n^2 = 7n -2`

`\rightarrow 5n^2 - 7n +2=0`

`\rightarrow 5n^2 - 5n -2n+2=0`

`\rightarrow 5n(n - 1) -2(n-1)=0`

`\rightarrow (5n-2)(n-1)=0`

`\rightarrow 5n-2= 0,\: n-1=0`

`\rightarrow 5n= 2,\: n=1`

`\rightarrow n= (2)/(5) ,\: n=1`