x^2-0.19x-1=0

Solution for x^2-0.19x-1=0 equation:

x^2-0.19x-1=0

a = 1; b = -0.19; c = -1;
Δ = b2-4ac
Δ = -0.192-4·1·(-1)
Δ = 4.0361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-0.19)-\sqrt{4.0361}}{2*1}=\frac{0.19-\sqrt{4.0361}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.19)+\sqrt{4.0361}}{2*1}=\frac{0.19+\sqrt{4.0361}}{2}
$