To solve the quadratic equation \(2x^2 - 5x = 6\), we first rearrange it to the standard form of a quadratic equation:
\[ 2x^2 - 5x - 6 = 0 \]
Next, we can use the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
In our equation, \(a = 2\), \(b = -5\), and \(c = -6\). We first calculate the discriminant:
\[ b^2 - 4ac = (-5)^2 - 4 \cdot 2 \cdot (-6) = 25 + 48 = 73 \]
Now we can substitute the values into the quadratic formula:
\[ x = \frac{-(-5) \pm \sqrt{73}}{2 \cdot 2} = \frac{5 \pm \sqrt{73}}{4} \]
Now, we approximate \(\sqrt{73}\). The square root of 73 is approximately 8.544.
Using this value, we calculate the two possible solutions for \(x\):
\[ x_1 = \frac{5 + 8.544}{4} = \frac{13.544}{4} \approx 3.386 \]
\[ x_2 = \frac{5 - 8.544}{4} = \frac{-3.544}{4} \approx -0.886 \]
Rounding these values to the nearest hundredth, we get:
\[ x_1 \approx 3.39 \quad \text{and} \quad x_2 \approx -0.89 \]
Thus, the solutions to the quadratic equation \(2x^2 - 5x - 6 = 0\) rounded to the nearest hundredth are approximately \(3.39\) and \(-0.89\).