-5z^2-10z+24=0

Solution for -5z^2-10z+24=0 equation:

-5z^2-10z+24=0

a = -5; b = -10; c = +24;
Δ = b2-4ac
Δ = -102-4·(-5)·24
Δ = 580
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:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{145}}{2*-5}=\frac{10-2\sqrt{145}}{-10}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{145}}{2*-5}=\frac{10+2\sqrt{145}}{-10}
$