which of the following is a solution to the quadratic equation 2x^2 - 5x = 6

Answer 1

To find the solutions to the quadratic equation $2x^2-5x=6$, we first rewrite it in standard form:

$$2x^2-5x-6=0$$

Next, we can solve this equation using the quadratic formula:

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

In our equation, $a=2$, $b=-5$, and $c=-6$.

Now, we can calculate the discriminant:

$$b^2-4ac=(-5{)}^2-4(2)(-6)=25+48=73$$

Since the discriminant is positive, we have two real solutions. Now we can apply the quadratic formula:

$$x=\frac{-(-5)\pm \sqrt{73}}{2\cdot 2}=\frac{5\pm \sqrt{73}}{4}$$

Thus, the two solutions are:

$$x=\frac{5+\sqrt{73}}{4}\text{and}x=\frac{5-\sqrt{73}}{4}$$

If you have specific answer options, you can compare them to $\frac{5+\sqrt{73}}{4}$ and $\frac{5-\sqrt{73}}{4}$ to see if any match.