40n^2=230^3

Solution for 40n^2=230^3 equation:

40n^2=230^3

We move all terms to the left:

40n^2-(230^3)=0

We add all the numbers together, and all the variables

40n^2-12167000=0

a = 40; b = 0; c = -12167000;
Δ = b2-4ac
Δ = 02-4·40·(-12167000)
Δ = 1946720000
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:

$\sqrt{\Delta}=\sqrt{1946720000}=\sqrt{84640000*23}=\sqrt{84640000}*\sqrt{23}=9200\sqrt{23}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-9200\sqrt{23}}{2*40}=\frac{0-9200\sqrt{23}}{80}
=-\frac{9200\sqrt{23}}{80}
=-115\sqrt{23}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+9200\sqrt{23}}{2*40}=\frac{0+9200\sqrt{23}}{80}
=\frac{9200\sqrt{23}}{80}
=115\sqrt{23}
$