The quadratic formula shown above provides the solutions for a quadratic equation in standard form, that is

ax2 + bx + c = 0,

where a  0

Write the standard form of a quadratic equation.

ax2 + bx + c = 0

Subtract c from both sides.

ax2 + bx = -c

Divide both sides by a.

Add (ᵇ⁄₂ₐ)2 to both sides to get a perfect square on the left side.

Take square root on both sides.

Example 1 :

x2 – 5x + 6 = 0

Solution :

Comparing ax2 + bx + c = 0 and x2 – 5x + 6 = 0, we get

a = 1, b = -5, c = 6

Substitute a = 1, b = -5 and c = 6.

x = 3  or  2

Example 2 :

x2 – 2x – 2 = 0

Solution :

Comparing ax2 + bx + c = 0 and x2 – 2x – 2 = 0, we get

a = 1, b = -2, c = -2

Substitute the above values into the quadratic formula.

x = 1 + √3  or  1 - √3

Example 3 :

3x2 – 4x – 9 = 0

Solution :

Comparing ax2 + bx + c = 0 and x2 – 2x – 2 = 0, we get

a = 3, b = -4, c = -9

Substitute the above values into the quadratic formula.

Example 4 :

x2 - 9x + 27 = 0

Solution :

Comparing ax2 + bx + c = 0 and x2 - 9x + 27 = 0, we get

a = 1, b = -9, c = 27

Substitute the above values into the quadratic formula.

Example 5 :

3x2 - 2√3x - 5 = 0

Solution :

Comparing ax2 + bx + c = 0 and x2 - 9x + 27 = 0, we get

a = 3, b = -2√3, c = -5

Substitute the above values into the quadratic formula.

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