Question

2x² + 9x - 5 = 0

Explanation:

Step1: Identify quadratic coefficients

For $2x^2 + 9x - 5 = 0$, $a=2$, $b=9$, $c=-5$

Step2: Use quadratic formula

Quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Step3: Calculate discriminant

$\Delta = b^2 - 4ac = 9^2 - 4\times2\times(-5) = 81 + 40 = 121$

Step4: Substitute into formula

$x = \frac{-9 \pm \sqrt{121}}{2\times2} = \frac{-9 \pm 11}{4}$

Step5: Solve for two roots

First root: $x_1 = \frac{-9 + 11}{4} = \frac{2}{4} = \frac{1}{2}$
Second root: $x_2 = \frac{-9 - 11}{4} = \frac{-20}{4} = -5$

Answer:

$x = \frac{1}{2}$ or $x = -5$