40x^2-10x-1=0

Solution for 40x^2-10x-1=0 equation:

40x^2-10x-1=0

a = 40; b = -10; c = -1;
Δ = b2-4ac
Δ = -102-4·40·(-1)
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{65}}{2*40}=\frac{10-2\sqrt{65}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{65}}{2*40}=\frac{10+2\sqrt{65}}{80}
$