8b^2-44b+1=0

Solution for 8b^2-44b+1=0 equation:

8b^2-44b+1=0

a = 8; b = -44; c = +1;
Δ = b2-4ac
Δ = -442-4·8·1
Δ = 1904
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1904}=\sqrt{16*119}=\sqrt{16}*\sqrt{119}=4\sqrt{119}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{119}}{2*8}=\frac{44-4\sqrt{119}}{16}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{119}}{2*8}=\frac{44+4\sqrt{119}}{16}
$