20n^2-38-30=0

Solution for 20n^2-38-30=0 equation:

20n^2-38-30=0

We add all the numbers together, and all the variables

20n^2-68=0

a = 20; b = 0; c = -68;
Δ = b2-4ac
Δ = 02-4·20·(-68)
Δ = 5440
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:

$\sqrt{\Delta}=\sqrt{5440}=\sqrt{64*85}=\sqrt{64}*\sqrt{85}=8\sqrt{85}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{85}}{2*20}=\frac{0-8\sqrt{85}}{40}
=-\frac{8\sqrt{85}}{40}
=-\frac{\sqrt{85}}{5}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{85}}{2*20}=\frac{0+8\sqrt{85}}{40}
=\frac{8\sqrt{85}}{40}
=\frac{\sqrt{85}}{5}
$