5z^2-6z-1=0

Solution for 5z^2-6z-1=0 equation:

5z^2-6z-1=0

a = 5; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·5·(-1)
Δ = 56
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{14}}{2*5}=\frac{6-2\sqrt{14}}{10}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{14}}{2*5}=\frac{6+2\sqrt{14}}{10}
$