Multiply $ \dfrac{1}{2} $ by $ 10x^2-4 $ to get $ \dfrac{ 10x^2-4 }{ 2 } $.

Step 1: Write $ 10x^2-4 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{1}{2} \cdot 10x^2-4 & \xlongequal{\text{Step 1}} \frac{1}{2} \cdot \frac{10x^2-4}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 1 \cdot \left( 10x^2-4 \right) }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 10x^2-4 }{ 2 } \end{aligned} $$

Subtract $ \dfrac{10x^2-4}{2} $ from $ 5x^2+7x $ to get $ \dfrac{ \color{purple}{ 14x+4 } }{ 2 }$.

Step 1: Write $ 5x^2+7x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 2 }$.

$$ \begin{aligned} 5x^2+7x- \frac{10x^2-4}{2} & \xlongequal{\text{Step 1}} \frac{5x^2+7x}{\color{red}{1}} - \frac{10x^2-4}{2} = \frac{ \left( 5x^2+7x \right) \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} - \frac{ 10x^2-4 }{ 2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 10x^2+14x } }{ 2 } - \frac{ \color{purple}{ 10x^2-4 } }{ 2 }=\frac{ \color{purple}{ 10x^2+14x - \left( 10x^2-4 \right) } }{ 2 } = \\[1ex] &=\frac{ \color{purple}{ 14x+4 } }{ 2 } \end{aligned} $$