Solve the Quadratic Equation: 2x² + x - 10 = 0

To solve the quadratic equation $2x^2 + x - 10 = 0$, we'll apply the quadratic formula. The equation is in standard form $ax^2 + bx + c = 0$, where:

• $a = 2$
• $b = 1$
• $c = -10$

Now, substitute these values into the quadratic formula:
$x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a}$

Step 1: Calculate the discriminant:

$b^2 - 4ac = 1^2 - 4 \times 2 \times (-10) = 1 + 80 = 81$

Step 2: Take the square root of the discriminant:

$\sqrt{81} = 9$

Step 3: Solve for $x$ using the quadratic formula:

• $x_1 = \frac{{-1 + 9}}{4} = \frac{8}{4} = 2$
• $x_2 = \frac{{-1 - 9}}{4} = \frac{-10}{4} = -\frac{5}{2} = -2\frac{1}{2}$

The solutions to the equation $2x^2 + x - 10 = 0$ are $x_1 = 2$ and $x_2 = -2\frac{1}{2}$.

Therefore, the correct choice from the provided options is

$x_1=-2\frac{1}{2}, x_2=2$