4.5x2+9x+4.5=1

Solution for 4.5x2+9x+4.5=1 equation:

4.5x^2+9x+4.5=1

We move all terms to the left:

4.5x^2+9x+4.5-(1)=0

We add all the numbers together, and all the variables

4.5x^2+9x+3.5=0

a = 4.5; b = 9; c = +3.5;
Δ = b2-4ac
Δ = 92-4·4.5·3.5
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{-(9)-3\sqrt{2}}{2*4.5}=\frac{-9-3\sqrt{2}}{9}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{2}}{2*4.5}=\frac{-9+3\sqrt{2}}{9}
$