x^2-4-5x+4.5=0

Solution for x^2-4-5x+4.5=0 equation:

x^2-4-5x+4.5=0

We add all the numbers together, and all the variables

x^2-5x+0.5=0

a = 1; b = -5; c = +0.5;
Δ = b2-4ac
Δ = -52-4·1·0.5
Δ = 23
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{-(-5)-\sqrt{23}}{2*1}=\frac{5-\sqrt{23}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{23}}{2*1}=\frac{5+\sqrt{23}}{2}
$