x^2+9x+4.5=2.5

Solution for x^2+9x+4.5=2.5 equation:

x^2+9x+4.5=2.5

We move all terms to the left:

x^2+9x+4.5-(2.5)=0

We add all the numbers together, and all the variables

x^2+9x+2=0

a = 1; b = 9; c = +2;
Δ = b2-4ac
Δ = 92-4·1·2
Δ = 73
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{-(9)-\sqrt{73}}{2*1}=\frac{-9-\sqrt{73}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{73}}{2*1}=\frac{-9+\sqrt{73}}{2}
$