23*n2=200

Solution for 23*n2=200 equation:

23n^2=200

We move all terms to the left:

23n^2-(200)=0

a = 23; b = 0; c = -200;
Δ = b2-4ac
Δ = 02-4·23·(-200)
Δ = 18400
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:

$\sqrt{\Delta}=\sqrt{18400}=\sqrt{400*46}=\sqrt{400}*\sqrt{46}=20\sqrt{46}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{46}}{2*23}=\frac{0-20\sqrt{46}}{46}
=-\frac{20\sqrt{46}}{46}
=-\frac{10\sqrt{46}}{23}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{46}}{2*23}=\frac{0+20\sqrt{46}}{46}
=\frac{20\sqrt{46}}{46}
=\frac{10\sqrt{46}}{23}
$