4x^2-32x+1=0

Solution for 4x^2-32x+1=0 equation:

4x^2-32x+1=0

a = 4; b = -32; c = +1;
Δ = b2-4ac
Δ = -322-4·4·1
Δ = 1008
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:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-12\sqrt{7}}{2*4}=\frac{32-12\sqrt{7}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+12\sqrt{7}}{2*4}=\frac{32+12\sqrt{7}}{8}
$