-5z^2-2z+5=0

Solution for -5z^2-2z+5=0 equation:

-5z^2-2z+5=0

a = -5; b = -2; c = +5;
Δ = b2-4ac
Δ = -22-4·(-5)·5
Δ = 104
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:

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