2x^2+6x+9=22.5

Solution for 2x^2+6x+9=22.5 equation:

2x^2+6x+9=22.5

We move all terms to the left:

2x^2+6x+9-(22.5)=0

We add all the numbers together, and all the variables

2x^2+6x-13.5=0

a = 2; b = 6; c = -13.5;
Δ = b2-4ac
Δ = 62-4·2·(-13.5)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-12}{2*2}=\frac{-18}{4}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+12}{2*2}=\frac{6}{4}
=1+1/2
$