x2-4x+3=0

To solve the quadratic equation \(x^2 - 4x + 3 = 0\), we can use the quadratic formula:

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

For the equation \( ax^2 + bx + c = 0 \), we have:

• \( a = 1 \)
• \( b = -4 \)
• \( c = 3 \)

Substituting these values into the quadratic formula gives:

\[ x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4 \times 1 \times 3}}{2 \times 1} \]

\[ x = \frac{4 \pm \sqrt{16 - 12}}{2} \]

\[ x = \frac{4 \pm \sqrt{4}}{2} \]

\[ x = \frac{4 \pm 2}{2} \]

This results in two solutions:

1. \( x = \frac{4 + 2}{2} = 3 \)
2. \( x = \frac{4 - 2}{2} = 1 \)

Therefore, the solutions are \( x = 3 \) and \( x = 1 \).