2=-16x^2+64

Solution for 2=-16x^2+64 equation:

2=-16x^2+64

We move all terms to the left:

2-(-16x^2+64)=0

We get rid of parentheses

16x^2-64+2=0

We add all the numbers together, and all the variables

16x^2-62=0

a = 16; b = 0; c = -62;
Δ = b2-4ac
Δ = 02-4·16·(-62)
Δ = 3968
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:

$\sqrt{\Delta}=\sqrt{3968}=\sqrt{64*62}=\sqrt{64}*\sqrt{62}=8\sqrt{62}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{62}}{2*16}=\frac{0-8\sqrt{62}}{32}
=-\frac{8\sqrt{62}}{32}
=-\frac{\sqrt{62}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{62}}{2*16}=\frac{0+8\sqrt{62}}{32}
=\frac{8\sqrt{62}}{32}
=\frac{\sqrt{62}}{4}
$