2x2+5x-6=0

To solve the quadratic equation \(2x^2 + 5x - 6 = 0\), we can use the quadratic formula, which is given by:

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

where \(a\), \(b\), and \(c\) are the coefficients from the equation \(ax^2 + bx + c = 0\).

In this equation, we have:

• \(a = 2\)
• \(b = 5\)
• \(c = -6\)

Now, we can calculate the discriminant (\(b^2 - 4ac\)):

\[ b^2 - 4ac = 5^2 - 4(2)(-6) = 25 + 48 = 73 \]

Now substituting the values into the quadratic formula:

\[ x = \frac{-5 \pm \sqrt{73}}{2(2)} = \frac{-5 \pm \sqrt{73}}{4} \]

Therefore, the solutions to the equation \(2x^2 + 5x - 6 = 0\) are:

\[ x = \frac{-5 + \sqrt{73}}{4} \quad \text{and} \quad x = \frac{-5 - \sqrt{73}}{4} \]

These are the two solutions for the value of \(x\).