228=(n/2)(7n-1)

Solution for 228=(n/2)(7n-1) equation:

228=(n/2)(7n-1)

We move all terms to the left:

228-((n/2)(7n-1))=0


Domain of the equation: 2)(7n-1))!=0

n∈R


We add all the numbers together, and all the variables

-((+n/2)(7n-1))+228=0

We multiply parentheses ..

-((+7n^2-1n))+228=0


We calculate terms in parentheses: -((+7n^2-1n)), so:

(+7n^2-1n)

We get rid of parentheses

7n^2-1n

Back to the equation:

-(7n^2-1n)


We get rid of parentheses

-7n^2+1n+228=0

We add all the numbers together, and all the variables

-7n^2+n+228=0

a = -7; b = 1; c = +228;
Δ = b2-4ac
Δ = 12-4·(-7)·228
Δ = 6385
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{6385}}{2*-7}=\frac{-1-\sqrt{6385}}{-14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{6385}}{2*-7}=\frac{-1+\sqrt{6385}}{-14}
$