Hi Assassinbeast!
A fraction remains the same if you multiply numerator and denominator both by the same number.
And when you want to add fraction, you first have to make the denominators the same, and then you can add the numerators.
In your case:
$\displaystyle \frac{b^2}{4a} - \frac{b^2}{2a} + c$
$\displaystyle = \frac{b^2}{4a} - \frac{b^2 \cdot 2}{2a \cdot 2} + c \cdot \frac {4a}{4a}$
$\displaystyle = \frac{b^2}{4a} - \frac{2 b^2}{4a} + \frac {4ac}{4a}$
$\displaystyle = \frac{b^2 - 2 b^2 + 4ac}{4a}$