Solve $\color{blue}{12x^2+10x-1 = 0}$ using the Quadratic Formula.
Step 1: 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:
$$ a = 12, \,\, b = 10, \,\, c = -1 $$Step 2: Plug in the values for $ a $, $ b $, and $ c $ into the quadratic formula.
$$ \begin{aligned} x_1,x_2 &= \frac{-b \pm \sqrt{b^2-4ac}}{2a} \\[1 em] x_1,x_2 &= \frac{ -10 \pm \sqrt{ 10 ^2 - 4 \cdot 12 \cdot (-1)} }{ 2 \cdot 12 } \end{aligned} $$Step 3: Simplify expression under the square root.
$$ x_1,x_2 = \frac{ -10 \pm \sqrt{ 148 } }{ 24 } $$Step 4: Solve for $ x $
$$ \begin{aligned} & \color{blue}{ x_1 = \frac{ -10~-~\sqrt{ 148 } }{ 24 } = -\frac{ 5 }{ 12 }-\frac{\sqrt{ 37 }}{ 12 } } \\\\ & \color{blue}{ x_2 = \frac{ -10~+~\sqrt{ 148 } }{ 24 } = -\frac{ 5 }{ 12 }+\frac{\sqrt{ 37 }}{ 12 } } \end{aligned} $$