z^2-1.5z-1=0

Solution for z^2-1.5z-1=0 equation:

z^2-1.5z-1=0

a = 1; b = -1.5; c = -1;
Δ = b2-4ac
Δ = -1.52-4·1·(-1)
Δ = 6.25
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{-(-1.5)-\sqrt{6.25}}{2*1}=\frac{1.5-\sqrt{6.25}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.5)+\sqrt{6.25}}{2*1}=\frac{1.5+\sqrt{6.25}}{2}
$