Question

2x² + 3x - 5 = 0

Explanation:

Step1: Identify the quadratic equation

The equation is \(2x^{2}+3x - 15=0\) (assuming the last term is \(- 15\) as the hand - written might have a typo, standard quadratic form \(ax^{2}+bx + c = 0\) here \(a = 2\), \(b=3\), \(c=- 15\))

Step2: Use the quadratic formula

The quadratic formula is \(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\)

First, calculate the discriminant \(\Delta=b^{2}-4ac\)

Substitute \(a = 2\), \(b = 3\), \(c=-15\) into the discriminant formula:

\(\Delta=(3)^{2}-4\times2\times(-15)=9 + 120=129\)

Then, substitute \(a = 2\), \(b = 3\), \(\Delta = 129\) into the quadratic formula:

\(x=\frac{-3\pm\sqrt{129}}{2\times2}=\frac{-3\pm\sqrt{129}}{4}\)

Answer:

\(x=\frac{-3 + \sqrt{129}}{4}\) or \(x=\frac{-3-\sqrt{129}}{4}\) (If we assume the equation is \(2x^{2}+3x - 15 = 0\), if the original equation has a different constant term, the solution will change accordingly)