8-2x^2=-81

Solution for 8-2x^2=-81 equation:

8-2x^2=-81

We move all terms to the left:

8-2x^2-(-81)=0

We add all the numbers together, and all the variables

-2x^2+89=0

a = -2; b = 0; c = +89;
Δ = b2-4ac
Δ = 02-4·(-2)·89
Δ = 712
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:

$\sqrt{\Delta}=\sqrt{712}=\sqrt{4*178}=\sqrt{4}*\sqrt{178}=2\sqrt{178}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{178}}{2*-2}=\frac{0-2\sqrt{178}}{-4}
=-\frac{2\sqrt{178}}{-4}
=-\frac{\sqrt{178}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{178}}{2*-2}=\frac{0+2\sqrt{178}}{-4}
=\frac{2\sqrt{178}}{-4}
=\frac{\sqrt{178}}{-2}
$