Solve Using the Quadratic Formula a^2-5a+6=0

$a^{2} - 5 a + 6 = 0$

Step 1

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 2

Substitute the values $a = 1$ , $b = - 5$ , and $c = 6$ into the quadratic formula and solve for $a$ .

$\frac{5 \pm \sqrt{{(- 5)}^{2} - 4 \cdot (1 \cdot 6)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 5$ to the power of $2$ .

$a = \frac{5 \pm \sqrt{25 - 4 \cdot 1 \cdot 6}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 6$ .

Multiply $- 4$ by $1$ .

$a = \frac{5 \pm \sqrt{25 - 4 \cdot 6}}{2 \cdot 1}$

Multiply $- 4$ by $6$ .

$a = \frac{5 \pm \sqrt{25 - 24}}{2 \cdot 1}$

Subtract $24$ from $25$ .

$a = \frac{5 \pm \sqrt{1}}{2 \cdot 1}$

Any root of $1$ is $1$ .

$a = \frac{5 \pm 1}{2 \cdot 1}$

Multiply $2$ by $1$ .

$a = \frac{5 \pm 1}{2}$

Step 4

The final answer is the combination of both solutions.

$a = 3, 2$