-8z^2-5z=-5

Solution for -8z^2-5z=-5 equation:

-8z^2-5z=-5

We move all terms to the left:

-8z^2-5z-(-5)=0

We add all the numbers together, and all the variables

-8z^2-5z+5=0

a = -8; b = -5; c = +5;
Δ = b2-4ac
Δ = -52-4·(-8)·5
Δ = 185
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{185}}{2*-8}=\frac{5-\sqrt{185}}{-16}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{185}}{2*-8}=\frac{5+\sqrt{185}}{-16}
$