1=49-64u^2

Solution for 1=49-64u^2 equation:

1=49-64u^2

We move all terms to the left:

1-(49-64u^2)=0

We get rid of parentheses

64u^2-49+1=0

We add all the numbers together, and all the variables

64u^2-48=0

a = 64; b = 0; c = -48;
Δ = b2-4ac
Δ = 02-4·64·(-48)
Δ = 12288
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12288}=\sqrt{4096*3}=\sqrt{4096}*\sqrt{3}=64\sqrt{3}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-64\sqrt{3}}{2*64}=\frac{0-64\sqrt{3}}{128}
=-\frac{64\sqrt{3}}{128}
=-\frac{\sqrt{3}}{2}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+64\sqrt{3}}{2*64}=\frac{0+64\sqrt{3}}{128}
=\frac{64\sqrt{3}}{128}
=\frac{\sqrt{3}}{2}
$