29540=1543(n*14)(n*21)

Solution for 29540=1543(n*14)(n*21) equation:

29540=1543(n*14)(n*21)

We move all terms to the left:

29540-(1543(n*14)(n*21))=0

We add all the numbers together, and all the variables

-(1543(+n*14)(+n*21))+29540=0

We multiply parentheses ..

-(1543(+294n^2))+29540=0


We calculate terms in parentheses: -(1543(+294n^2)), so:

1543(+294n^2)

We multiply parentheses

453642n^2

Back to the equation:

-(453642n^2)


a = -453642; b = 0; c = +29540;
Δ = b2-4ac
Δ = 02-4·(-453642)·29540
Δ = 53602338720
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{53602338720}=\sqrt{784*68370330}=\sqrt{784}*\sqrt{68370330}=28\sqrt{68370330}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28\sqrt{68370330}}{2*-453642}=\frac{0-28\sqrt{68370330}}{-907284}
=-\frac{28\sqrt{68370330}}{-907284}
=-\frac{\sqrt{68370330}}{-32403}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28\sqrt{68370330}}{2*-453642}=\frac{0+28\sqrt{68370330}}{-907284}
=\frac{28\sqrt{68370330}}{-907284}
=\frac{\sqrt{68370330}}{-32403}
$