x^2=-2x+4.5

Solution for x^2=-2x+4.5 equation:

x^2=-2x+4.5

We move all terms to the left:

x^2-(-2x+4.5)=0

We get rid of parentheses

x^2+2x-4.5=0

a = 1; b = 2; c = -4.5;
Δ = b2-4ac
Δ = 22-4·1·(-4.5)
Δ = 22
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{-(2)-\sqrt{22}}{2*1}=\frac{-2-\sqrt{22}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+\sqrt{22}}{2*1}=\frac{-2+\sqrt{22}}{2}
$