2z^2+31z-16=0

Solution for 2z^2+31z-16=0 equation:

2z^2+31z-16=0

a = 2; b = 31; c = -16;
Δ = b2-4ac
Δ = 312-4·2·(-16)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-33}{2*2}=\frac{-64}{4}
=-16
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+33}{2*2}=\frac{2}{4}
=1/2
$