50n^2-19=0

Solution for 50n^2-19=0 equation:

50n^2-19=0

a = 50; b = 0; c = -19;
Δ = b2-4ac
Δ = 02-4·50·(-19)
Δ = 3800
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:

$\sqrt{\Delta}=\sqrt{3800}=\sqrt{100*38}=\sqrt{100}*\sqrt{38}=10\sqrt{38}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{38}}{2*50}=\frac{0-10\sqrt{38}}{100}
=-\frac{10\sqrt{38}}{100}
=-\frac{\sqrt{38}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{38}}{2*50}=\frac{0+10\sqrt{38}}{100}
=\frac{10\sqrt{38}}{100}
=\frac{\sqrt{38}}{10}
$