2=1776-16x^2

Solution for 2=1776-16x^2 equation:

2=1776-16x^2

We move all terms to the left:

2-(1776-16x^2)=0

We get rid of parentheses

16x^2-1776+2=0

We add all the numbers together, and all the variables

16x^2-1774=0

a = 16; b = 0; c = -1774;
Δ = b2-4ac
Δ = 02-4·16·(-1774)
Δ = 113536
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:

$\sqrt{\Delta}=\sqrt{113536}=\sqrt{64*1774}=\sqrt{64}*\sqrt{1774}=8\sqrt{1774}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{1774}}{2*16}=\frac{0-8\sqrt{1774}}{32}
=-\frac{8\sqrt{1774}}{32}
=-\frac{\sqrt{1774}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{1774}}{2*16}=\frac{0+8\sqrt{1774}}{32}
=\frac{8\sqrt{1774}}{32}
=\frac{\sqrt{1774}}{4}
$