-6-5n^2=-82

Solution for -6-5n^2=-82 equation:

-6-5n^2=-82

We move all terms to the left:

-6-5n^2-(-82)=0

We add all the numbers together, and all the variables

-5n^2+76=0

a = -5; b = 0; c = +76;
Δ = b2-4ac
Δ = 02-4·(-5)·76
Δ = 1520
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:

$\sqrt{\Delta}=\sqrt{1520}=\sqrt{16*95}=\sqrt{16}*\sqrt{95}=4\sqrt{95}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{95}}{2*-5}=\frac{0-4\sqrt{95}}{-10}
=-\frac{4\sqrt{95}}{-10}
=-\frac{2\sqrt{95}}{-5}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{95}}{2*-5}=\frac{0+4\sqrt{95}}{-10}
=\frac{4\sqrt{95}}{-10}
=\frac{2\sqrt{95}}{-5}
$