9f^2-8f+1=0

Solution for 9f^2-8f+1=0 equation:

9f^2-8f+1=0

a = 9; b = -8; c = +1;
Δ = b2-4ac
Δ = -82-4·9·1
Δ = 28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{7}}{2*9}=\frac{8-2\sqrt{7}}{18}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{7}}{2*9}=\frac{8+2\sqrt{7}}{18}
$