-8-4x^2=-216

Solution for -8-4x^2=-216 equation:

-8-4x^2=-216

We move all terms to the left:

-8-4x^2-(-216)=0

We add all the numbers together, and all the variables

-4x^2+208=0

a = -4; b = 0; c = +208;
Δ = b2-4ac
Δ = 02-4·(-4)·208
Δ = 3328
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3328}=\sqrt{256*13}=\sqrt{256}*\sqrt{13}=16\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{13}}{2*-4}=\frac{0-16\sqrt{13}}{-8}
=-\frac{16\sqrt{13}}{-8}
=-\frac{2\sqrt{13}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{13}}{2*-4}=\frac{0+16\sqrt{13}}{-8}
=\frac{16\sqrt{13}}{-8}
=\frac{2\sqrt{13}}{-1}
$