-882=n(-4n+42)

Solution for -882=n(-4n+42) equation:

-882=n(-4n+42)

We move all terms to the left:

-882-(n(-4n+42))=0


We calculate terms in parentheses: -(n(-4n+42)), so:

n(-4n+42)

We multiply parentheses

-4n^2+42n

Back to the equation:

-(-4n^2+42n)


We get rid of parentheses

4n^2-42n-882=0

a = 4; b = -42; c = -882;
Δ = b2-4ac
Δ = -422-4·4·(-882)
Δ = 15876
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15876}=126$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-126}{2*4}=\frac{-84}{8}
=-10+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+126}{2*4}=\frac{168}{8}
=21
$