5n2=50

Solution for 5n2=50 equation:

5n^2=50

We move all terms to the left:

5n^2-(50)=0

a = 5; b = 0; c = -50;
Δ = b2-4ac
Δ = 02-4·5·(-50)
Δ = 1000
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:

$\sqrt{\Delta}=\sqrt{1000}=\sqrt{100*10}=\sqrt{100}*\sqrt{10}=10\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{10}}{2*5}=\frac{0-10\sqrt{10}}{10}
=-\frac{10\sqrt{10}}{10}
=-\sqrt{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{10}}{2*5}=\frac{0+10\sqrt{10}}{10}
=\frac{10\sqrt{10}}{10}
=\sqrt{10}
$