x^2+4.5^2=9^2

Solution for x^2+4.5^2=9^2 equation:

x^2+4.5^2=9^2

We move all terms to the left:

x^2+4.5^2-(9^2)=0

We add all the numbers together, and all the variables

x^2-60.75=0

a = 1; b = 0; c = -60.75;
Δ = b2-4ac
Δ = 02-4·1·(-60.75)
Δ = 243
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:

$\sqrt{\Delta}=\sqrt{243}=\sqrt{81*3}=\sqrt{81}*\sqrt{3}=9\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-9\sqrt{3}}{2*1}=\frac{0-9\sqrt{3}}{2}
=-\frac{9\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+9\sqrt{3}}{2*1}=\frac{0+9\sqrt{3}}{2}
=\frac{9\sqrt{3}}{2}
$