6n(1+n)=8n-3(n-7)

Solution for 6n(1+n)=8n-3(n-7) equation:

6n(1+n)=8n-3(n-7)

We move all terms to the left:

6n(1+n)-(8n-3(n-7))=0

We add all the numbers together, and all the variables

6n(n+1)-(8n-3(n-7))=0

We multiply parentheses

6n^2+6n-(8n-3(n-7))=0


We calculate terms in parentheses: -(8n-3(n-7)), so:

8n-3(n-7)

We multiply parentheses

8n-3n+21

We add all the numbers together, and all the variables

5n+21

Back to the equation:

-(5n+21)


We get rid of parentheses

6n^2+6n-5n-21=0

We add all the numbers together, and all the variables

6n^2+n-21=0

a = 6; b = 1; c = -21;
Δ = b2-4ac
Δ = 12-4·6·(-21)
Δ = 505
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{505}}{2*6}=\frac{-1-\sqrt{505}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{505}}{2*6}=\frac{-1+\sqrt{505}}{12}
$