How to Solve a Quadratic Equation Using the Quadratic Formula.

In this post, we'll learn how to solve any quadratic equation using the famous quadratic formula:

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

Let's solve the equation:

\[ 2x^2 + 3x - 5 = 0 \]

Here, we identify the coefficients:

• \( a = 2 \)
• \( b = 3 \)
• \( c = -5 \)

Substitute these into the formula:

\[ x = \frac{-3 \pm \sqrt{3^2 - 4(2)(-5)}}{2(2)} \] \[ x = \frac{-3 \pm \sqrt{9 + 40}}{4} \] \[ x = \frac{-3 \pm \sqrt{49}}{4} \] \[ x = \frac{-3 \pm 7}{4} \]

So, we have two solutions:

\[ x = \frac{-3 + 7}{4} = 1 \quad \text{and} \quad x = \frac{-3 - 7}{4} = -2.5 \]

✅ Final Answer: \( x = 1 \) or \( x = -2.5 \)