5f^2-8f-2=0

Solution for 5f^2-8f-2=0 equation:

5f^2-8f-2=0

a = 5; b = -8; c = -2;
Δ = b2-4ac
Δ = -82-4·5·(-2)
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{26}}{2*5}=\frac{8-2\sqrt{26}}{10}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{26}}{2*5}=\frac{8+2\sqrt{26}}{10}
$