x2+3x+2.25=6.75

Solution for x2+3x+2.25=6.75 equation:

x2+3x+2.25=6.75

We move all terms to the left:

x2+3x+2.25-(6.75)=0

We add all the numbers together, and all the variables

x^2+3x-4.5=0

a = 1; b = 3; c = -4.5;
Δ = b2-4ac
Δ = 32-4·1·(-4.5)
Δ = 27
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:

$\sqrt{\Delta}=\sqrt{27}=\sqrt{9*3}=\sqrt{9}*\sqrt{3}=3\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{3}}{2*1}=\frac{-3-3\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{3}}{2*1}=\frac{-3+3\sqrt{3}}{2}
$