We have the following coefficients of the quadratic function:
a = -10
b = 23
c = -12
And we need to find the roots to that function, using the formulas:
[tex]\begin{gathered} \frac{-b-\sqrt[]{b^{2}-4ac}}{2a} \\ \\ \frac{-b+\sqrt[]{b²-4ac}}{2a} \end{gathered}[/tex]
In order to do so, we need to replace each constant with its numerical value. So, we obtain:
[tex]\begin{gathered} \frac{-b-\sqrt[]{b²-4ac}}{2a}=\frac{-23-\sqrt[]{23^{2}-4(-10)(-12)}}{2(-10)} \\ \\ =\frac{-23-\sqrt[]{529-4(120)}}{-20}\text{ since the product of two negative numbers is positive} \\ \\ =\frac{-23-\sqrt[]{529-480}}{-20} \\ \\ =\frac{-23-\sqrt[]{49}}{-20} \\ \\ =\frac{-23-7}{-20} \\ \\ =\frac{-30}{-20} \\ \\ =\frac{3}{2} \end{gathered}[/tex]
Now, the second formula is similar to the first one: we only need to change the sign before the square root. Thus, we obtain:
[tex]\frac{-b+\sqrt[]{b²-4ac}}{2a}=\frac{-23+7}{-20}=\frac{-16}{-20}=\frac{4}{5}[/tex]
