X2-10x+24=0

To solve the quadratic equation \(x^2 - 10x + 24 = 0\), we can use the quadratic formula:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

Here, \(a = 1\), \(b = -10\), and \(c = 24\).

1. Calculate the discriminant \(b^2 - 4ac\):

\[ b^2 - 4ac = (-10)^2 - 4(1)(24) = 100 - 96 = 4 \]

2. Substitute the values into the quadratic formula:

\[ x = \frac{-(-10) \pm \sqrt{4}}{2(1)} = \frac{10 \pm 2}{2} \]

3. This gives us two possible solutions:

\[ x = \frac{10 + 2}{2} = \frac{12}{2} = 6 \]

\[ x = \frac{10 - 2}{2} = \frac{8}{2} = 4 \]

Therefore, the solutions to the equation \(x^2 - 10x + 24 = 0\) are:

\[ x = 6 \quad \text{and} \quad x = 4 \]