4.5=x^2

Solution for 4.5=x^2 equation:

4.5=x^2

We move all terms to the left:

4.5-(x^2)=0

We add all the numbers together, and all the variables

-1x^2+4.5=0

a = -1; b = 0; c = +4.5;
Δ = b2-4ac
Δ = 02-4·(-1)·4.5
Δ = 18
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{18}=\sqrt{9*2}=\sqrt{9}*\sqrt{2}=3\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{2}}{2*-1}=\frac{0-3\sqrt{2}}{-2}
=-\frac{3\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{2}}{2*-1}=\frac{0+3\sqrt{2}}{-2}
=\frac{3\sqrt{2}}{-2}
$