x^2+3x+4,5=225

Solution for x^2+3x+4,5=225 equation:

x^2+3x+4.5=225

We move all terms to the left:

x^2+3x+4.5-(225)=0

We add all the numbers together, and all the variables

x^2+3x-220.5=0

a = 1; b = 3; c = -220.5;
Δ = b2-4ac
Δ = 32-4·1·(-220.5)
Δ = 891
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:

$\sqrt{\Delta}=\sqrt{891}=\sqrt{81*11}=\sqrt{81}*\sqrt{11}=9\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-9\sqrt{11}}{2*1}=\frac{-3-9\sqrt{11}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+9\sqrt{11}}{2*1}=\frac{-3+9\sqrt{11}}{2}
$