Use the quadratic formula on 2x squared plus 5x minus 3 = 0. What are the solutions?

1. Read off a as 2, b as 5 and c as negative 3. 2. Work out the discriminant first: b squared is 25, and 4ac is 4 times 2 times negative 3, which is negative 24. 3. So the discriminant is 25 minus negative 24, which is 49. 4. The square root of 49 is 7, so the two branches are negative 5 plus 7 and negative 5 minus 7. 5. The denominator is 2a, which is 4. 6. The first branch gives 2 over 4, which is 0.5. 7. The second branch gives negative 12 over 4, which is negative 3. 8. Checking 0.5, twice 0.25 is 0.5, plus 2.5 is 3, minus 3 gives 0. 9. The pair with signs swapped comes from writing the numerator as positive 5 rather than negative 5. 10. The pair 3 and negative 2 comes from factoring the constant term without using the formula at all. _Source: OpenStax Intermediate Algebra (CC BY 4.0), section 9.3 Solve Quadratic Equations Using the Quadratic Formula_