Which of the following is a solution to the quadratic equation 2x^2−5x=6? Assume that the solution has been rounded to the nearest hundredth, if applicable.(1 point)

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, the coefficients are:

• \(a = 2\)
• \(b = -5\)
• \(c = -6\)

Now we plug these values into the quadratic formula:

1. Calculate the discriminant \(b^2 - 4ac\):

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

2. Now, substituting back into the formula:

\[ x = \frac{5 \pm \sqrt{73}}{4} \]

3. Calculate \(\sqrt{73}\):

\(\sqrt{73} \approx 8.54\) (to two decimal places)

4. Substitute back into the equation:

\[ x = \frac{5 \pm 8.54}{4} \]

Calculating the two possible values for \(x\):

• For the plus sign:

\[ x = \frac{5 + 8.54}{4} = \frac{13.54}{4} \approx 3.39 \]

• For the minus sign:

\[ x = \frac{5 - 8.54}{4} = \frac{-3.54}{4} \approx -0.89 \]

So the two solutions rounded to the nearest hundredth are approximately \(x \approx 3.39\) and \(x \approx -0.89\).

From the given options, the solution that matches our calculation is:

\(\boxed{-0.89}\)