Calculate the value of x in the following equation :-
`x^(2)-5x+6=0`

Answer

To solve the quadratic equation \( x^2 - 5x + 6 = 0 \), we can use the quadratic formula:

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

where \( a \), \( b \), and \( c \) are the coefficients from the equation \( ax^2 + bx + c = 0 \).

### Step 1: Identify the coefficients
From the equation \( x^2 - 5x + 6 = 0 \):
- \( a = 1 \) (coefficient of \( x^2 \))
- \( b = -5 \) (coefficient of \( x \))
- \( c = 6 \) (constant term)

### Step 2: Calculate the discriminant
The discriminant \( D \) is given by:

\[ D = b^2 - 4ac \]

Substituting the values:

\[ D = (-5)^2 - 4 \cdot 1 \cdot 6 \]
\[ D = 25 - 24 = 1 \]

### Step 3: Apply the quadratic formula
Now, substituting \( a \), \( b \), and \( D \) into the quadratic formula:

\[ x = \frac{-(-5) \pm \sqrt{1}}{2 \cdot 1} \]
\[ x = \frac{5 \pm 1}{2} \]

### Step 4: Calculate the two possible values for \( x \)
Now we will calculate the two possible values:

1. For \( x_1 \):
\[ x_1 = \frac{5 + 1}{2} = \frac{6}{2} = 3 \]

2. For \( x_2 \):
\[ x_2 = \frac{5 - 1}{2} = \frac{4}{2} = 2 \]

### Conclusion
The solutions to the equation \( x^2 - 5x + 6 = 0 \) are:

\[ x_1 = 3 \quad \text{and} \quad x_2 = 2 \]

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