Step 1: We can simplify equation by multiplying both sides by -1. After multiplying we have the following equation:
$$ \begin{aligned} -24x^2-60x+27 &= 0 \,\,\, / \color{orangered}{\cdot \, -1 } \\[0.9 em ] 24x^2+60x-27 &=0 \end{aligned} $$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:
$$ a = 24, \,\, b = 60, \,\, c = -27 $$Step 3: Plug in the values for $ a $, $ b $, and $ c $ into the quadratic formula.
$$ \begin{aligned} x_1,x_2 &= \frac{-b \pm \sqrt{b^2-4ac}}{2a} \\[1 em] x_1,x_2 &= \frac{ -60 \pm \sqrt{ 60 ^2 - 4 \cdot 24 \cdot (-27)} }{ 2 \cdot 24 } \end{aligned} $$Step 4: Simplify expression under the square root.
$$ x_1,x_2 = \frac{ -60 \pm \sqrt{ 6192 } }{ 48 } $$Step 5: Solve for $ x $
$$ \begin{aligned} & \color{blue}{ x_1 = \frac{ -60~-~\sqrt{ 6192 } }{ 48 } = -\frac{ 5 }{ 4 }-\frac{\sqrt{ 43 }}{ 4 } } \\\\ & \color{blue}{ x_2 = \frac{ -60~+~\sqrt{ 6192 } }{ 48 } = -\frac{ 5 }{ 4 }+\frac{\sqrt{ 43 }}{ 4 } } \end{aligned} $$