16x^2-64x+8=3

Solution for 16x^2-64x+8=3 equation:

16x^2-64x+8=3

We move all terms to the left:

16x^2-64x+8-(3)=0

We add all the numbers together, and all the variables

16x^2-64x+5=0

a = 16; b = -64; c = +5;
Δ = b2-4ac
Δ = -642-4·16·5
Δ = 3776
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:

$\sqrt{\Delta}=\sqrt{3776}=\sqrt{64*59}=\sqrt{64}*\sqrt{59}=8\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-8\sqrt{59}}{2*16}=\frac{64-8\sqrt{59}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+8\sqrt{59}}{2*16}=\frac{64+8\sqrt{59}}{32}
$