112=(24*42)/n2

Solution for 112=(24*42)/n2 equation:

112=(24*42)/n2

We move all terms to the left:

112-((24*42)/n2)=0


Domain of the equation: n2)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

-(1008/n2)+112=0

We get rid of parentheses

-1008/n2+112=0

We multiply all the terms by the denominator


112*n2-1008=0

We add all the numbers together, and all the variables

112n^2-1008=0

a = 112; b = 0; c = -1008;
Δ = b2-4ac
Δ = 02-4·112·(-1008)
Δ = 451584
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{451584}=672$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-672}{2*112}=\frac{-672}{224}
=-3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+672}{2*112}=\frac{672}{224}
=3
$