Quadratic Formula Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
Solve 2x2+3x−2=02x^2 + 3x - 2 = 0 using the quadratic formula.

Solution

  1. 1
    Identify a=2a = 2, b=3b = 3, c=−2c = -2.
  2. 2
    Apply the quadratic formula: x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
  3. 3
    Compute the discriminant: b2−4ac=9−4(2)(−2)=9+16=25b^2 - 4ac = 9 - 4(2)(-2) = 9 + 16 = 25.
  4. 4
    Substitute: x=−3±254=−3±54x = \frac{-3 \pm \sqrt{25}}{4} = \frac{-3 \pm 5}{4}.
  5. 5
    Two solutions: x=−3+54=12x = \frac{-3 + 5}{4} = \frac{1}{2} or x=−3−54=−2x = \frac{-3 - 5}{4} = -2.

Answer

x=12 or x=−2x = \frac{1}{2} \text{ or } x = -2
The quadratic formula works for any quadratic equation. The discriminant b2−4acb^2 - 4ac determines the number of solutions: positive means two real solutions, zero means one, and negative means no real solutions.

About Quadratic Formula

A formula giving the exact solutions to any quadratic equation ax2+bx+c=0ax^2 + bx + c = 0 directly from its three coefficients.

Learn more about Quadratic Formula →

More Quadratic Formula Examples

Example 1 easy

Solve [formula] by factoring.

Example 3 hard

Solve [formula] using the quadratic formula.

Example 4 easy

Solve [formula].

Example 5 hard

Solve [formula] and describe the solutions.

← All Quadratic Formula Examples Quadratic Formula Concept