x²-10x+24=0

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

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

In this equation, \( a = 1 \), \( b = -10 \), and \( c = 24 \).

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

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

2. Now substitute the values into the quadratic formula:

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

3. This gives us two possible solutions:

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

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

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

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