x^2-0.1x-0.9=0

Solution for x^2-0.1x-0.9=0 equation:

x^2-0.1x-0.9=0

a = 1; b = -0.1; c = -0.9;
Δ = b2-4ac
Δ = -0.12-4·1·(-0.9)
Δ = 3.61
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{-(-0.1)-\sqrt{3.61}}{2*1}=\frac{0.1-\sqrt{3.61}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.1)+\sqrt{3.61}}{2*1}=\frac{0.1+\sqrt{3.61}}{2}
$