-6-8r^2=-62

Solution for -6-8r^2=-62 equation:

-6-8r^2=-62

We move all terms to the left:

-6-8r^2-(-62)=0

We add all the numbers together, and all the variables

-8r^2+56=0

a = -8; b = 0; c = +56;
Δ = b2-4ac
Δ = 02-4·(-8)·56
Δ = 1792
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1792}=\sqrt{256*7}=\sqrt{256}*\sqrt{7}=16\sqrt{7}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{7}}{2*-8}=\frac{0-16\sqrt{7}}{-16}
=-\frac{16\sqrt{7}}{-16}
=-\frac{\sqrt{7}}{-1}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{7}}{2*-8}=\frac{0+16\sqrt{7}}{-16}
=\frac{16\sqrt{7}}{-16}
=\frac{\sqrt{7}}{-1}
$