-0.45z^2-0.4z+1=0

Solution for -0.45z^2-0.4z+1=0 equation:

-0.45z^2-0.4z+1=0

a = -0.45; b = -0.4; c = +1;
Δ = b2-4ac
Δ = -0.42-4·(-0.45)·1
Δ = 1.96
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{-(-0.4)-\sqrt{1.96}}{2*-0.45}=\frac{0.4-\sqrt{1.96}}{-0.9}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.4)+\sqrt{1.96}}{2*-0.45}=\frac{0.4+\sqrt{1.96}}{-0.9}
$