2x^2-3x+2.25=5

Solution for 2x^2-3x+2.25=5 equation:

2x^2-3x+2.25=5

We move all terms to the left:

2x^2-3x+2.25-(5)=0

We add all the numbers together, and all the variables

2x^2-3x-2.75=0

a = 2; b = -3; c = -2.75;
Δ = b2-4ac
Δ = -32-4·2·(-2.75)
Δ = 31
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{-(-3)-\sqrt{31}}{2*2}=\frac{3-\sqrt{31}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{31}}{2*2}=\frac{3+\sqrt{31}}{4}
$