32x2-32x+1=0

Solution for 32x2-32x+1=0 equation:

32x^2-32x+1=0

a = 32; b = -32; c = +1;
Δ = b2-4ac
Δ = -322-4·32·1
Δ = 896
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:

$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{14}}{2*32}=\frac{32-8\sqrt{14}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{14}}{2*32}=\frac{32+8\sqrt{14}}{64}
$