x^2-4.66x+1=0

Solution for x^2-4.66x+1=0 equation:

x^2-4.66x+1=0

a = 1; b = -4.66; c = +1;
Δ = b2-4ac
Δ = -4.662-4·1·1
Δ = 17.7156
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{-(-4.66)-\sqrt{17.7156}}{2*1}=\frac{4.66-\sqrt{17.7156}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4.66)+\sqrt{17.7156}}{2*1}=\frac{4.66+\sqrt{17.7156}}{2}
$