Medium📚 Quadratic Formula

Solve 2x² + 7x − 15 = 0 Step by Step

Algebra 1

Problem

Solve the quadratic equation: 2x² + 7x − 15 = 0

📝Step-by-Step Solution

Identify the coefficients

From 2x² + 7x − 15 = 0, we identify: a = 2, b = 7, c = −15

a = 2, b = 7, c = −15

Calculate the discriminant

Δ = b² − 4ac = (7)² − 4(2)(−15) = 49 + 120 = 169

Δ = 49 + 120 = 169

Apply the quadratic formula

x = (−b ± √Δ) / 2a = (−7 ± √169) / 2(2) = (−7 ± 13) / 4

x = (−7 ± 13) / 4

Calculate both solutions

x₁ = (−7 + 13) / 4 = 6/4 = 3/2 = 1.5. x₂ = (−7 − 13) / 4 = −20/4 = −5

x₁ = 1.5, x₂ = −5

✅Final Answer

x = 1.5 or x = −5

The discriminant Δ = 169 = 13² is a perfect square, which means the solutions are rational numbers. When a ≠ 1, remember to divide by 2a (which is 4 here), not just 2.

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