To eliminate decimals from the expression \((14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14)\), we can first convert all numbers to fractions and then simplify.
**Convert decimals to fractions**:
- \(2.25 = \frac{9}{4}\)
- \(0.75 = \frac{3}{4}\)
Now rewrite the expression:
\[
(14x^2 - 3x + \frac{9}{4}) + \left(\frac{3}{4}x^2 + 2x - 14\right)
\]
Next, combine like terms:
1. Combine the \(x^2\) terms:
\[
14x^2 + \frac{3}{4}x^2 = \left(14 + \frac{3}{4}\right)x^2 = \left(\frac{56}{4} + \frac{3}{4}\right)x^2 = \frac{59}{4}x^2
\]
2. Combine the \(x\) terms:
\[
-3x + 2x = (-3 + 2)x = -1x = -x
\]
3. Combine the constant terms:
\[
\frac{9}{4} - 14 = \frac{9}{4} - \frac{56}{4} = \frac{9 - 56}{4} = \frac{-47}{4}
\]
Now, putting it all together, we have:
\[
\frac{59}{4}x^2 - x - \frac{47}{4}
\]
To express it without decimals, you can multiply through by 4 to clear the fractions:
\[
4\left(\frac{59}{4}x^2 - x - \frac{47}{4}\right) = 59x^2 - 4x - 47
\]
So, the expression without decimals is:
\[
\boxed{59x^2 - 4x - 47}
\]