1-5n^2=-319

Solution for 1-5n^2=-319 equation:

1-5n^2=-319

We move all terms to the left:

1-5n^2-(-319)=0

We add all the numbers together, and all the variables

-5n^2+320=0

a = -5; b = 0; c = +320;
Δ = b2-4ac
Δ = 02-4·(-5)·320
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80}{2*-5}=\frac{-80}{-10}
=+8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80}{2*-5}=\frac{80}{-10}
=-8
$