Step 1: We can simplify equation by multiplying both sides by -1. After multiplying we have the following equation:

$$ \begin{aligned} -16x^2+48x+28 &= 0 \,\,\, / \color{orangered}{\cdot \, -1 } \\[0.9 em ] 16x^2-48x-28 &=0 \end{aligned} $$

Step 2: Read the values of $ a $, $ b $, and $ c $ from the quadratic equation: $ a $ is the number in front of $ x^2 $, $ b $ is the number in front of $ x $, $ c $ is the number at the end. In our case:

$$ a = 16, \,\, b = -48, \,\, c = -28 $$

Step 3: Plug in the values for $ a $, $ b $, and $ c $ into the quadratic formula.

$$ \begin{aligned} x_1,x_2 &= \frac{-b \pm \sqrt{b^2-4ac}}{2a} \\[1 em] x_1,x_2 &= \frac{ -(-48) \pm \sqrt{ (-48)^2 - 4 \cdot 16 \cdot (-28)} }{ 2 \cdot 16 } \end{aligned} $$

Step 4: Simplify expression under the square root.

$$ x_1,x_2 = \frac{ 48 \pm \sqrt{ 4096 } }{ 32 } $$

Step 5: Solve for $ x $

$$ \begin{aligned} & \color{blue}{ x_1 = \frac{ 48~-~\sqrt{ 4096 } }{ 32 } = -\frac{ 1 }{ 2 } } \\\\ & \color{blue}{ x_2 = \frac{ 48~+~\sqrt{ 4096 } }{ 32 } = \frac{ 7 }{ 2 } } \end{aligned} $$

Quadratic Equation Solver