-4-5n2=-334

Solution for -4-5n2=-334 equation:

-4-5n^2=-334

We move all terms to the left:

-4-5n^2-(-334)=0

We add all the numbers together, and all the variables

-5n^2+330=0

a = -5; b = 0; c = +330;
Δ = b2-4ac
Δ = 02-4·(-5)·330
Δ = 6600
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:

$\sqrt{\Delta}=\sqrt{6600}=\sqrt{100*66}=\sqrt{100}*\sqrt{66}=10\sqrt{66}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{66}}{2*-5}=\frac{0-10\sqrt{66}}{-10}
=-\frac{10\sqrt{66}}{-10}
=-\frac{\sqrt{66}}{-1}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{66}}{2*-5}=\frac{0+10\sqrt{66}}{-10}
=\frac{10\sqrt{66}}{-10}
=\frac{\sqrt{66}}{-1}
$