To solve the quadratic equation \(2x^2 - 5x = 6\), we first rearrange it into standard form:
\[ 2x^2 - 5x - 6 = 0 \]
Next, we can use the quadratic formula, which is given by:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
In our equation, \(a = 2\), \(b = -5\), and \(c = -6\). We will first calculate the discriminant \(b^2 - 4ac\):
\[ b^2 - 4ac = (-5)^2 - 4(2)(-6) = 25 + 48 = 73 \]
Now, we can substitute the values into the quadratic formula:
\[ x = \frac{-(-5) \pm \sqrt{73}}{2(2)} = \frac{5 \pm \sqrt{73}}{4} \]
This gives us two potential solutions:
\[ x_1 = \frac{5 + \sqrt{73}}{4}, \quad x_2 = \frac{5 - \sqrt{73}}{4} \]
These are the two solutions to the equation \(2x^2 - 5x = 6\). If you have specific options provided, please share them and I can indicate which one is correct.