x^2-3x+1=-0.9

Solution for x^2-3x+1=-0.9 equation:

x^2-3x+1=-0.9

We move all terms to the left:

x^2-3x+1-(-0.9)=0

We add all the numbers together, and all the variables

x^2-3x+1.9=0

a = 1; b = -3; c = +1.9;
Δ = b2-4ac
Δ = -32-4·1·1.9
Δ = 1.4
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{-(-3)-\sqrt{1.4}}{2*1}=\frac{3-\sqrt{1.4}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{1.4}}{2*1}=\frac{3+\sqrt{1.4}}{2}
$