2x^2-9x-2.25=-7+2.25

Solution for 2x^2-9x-2.25=-7+2.25 equation:

2x^2-9x-2.25=-7+2.25

We move all terms to the left:

2x^2-9x-2.25-(-7+2.25)=0

We add all the numbers together, and all the variables

2x^2-9x-2.25-(-4.75)=0

We add all the numbers together, and all the variables

2x^2-9x+2.5=0

a = 2; b = -9; c = +2.5;
Δ = b2-4ac
Δ = -92-4·2·2.5
Δ = 61
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{61}}{2*2}=\frac{9-\sqrt{61}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{61}}{2*2}=\frac{9+\sqrt{61}}{4}
$