Solve 2x² + 5x − 3 = 0

To solve the quadratic equation $2x^2 + 5x - 3 = 0$, we can use the quadratic formula.

The quadratic formula for an equation of the form $ax^2 + bx + c = 0$ is:
$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

In this equation, we have:
$a = 2$
$b = 5$
$c = -3$

Substitute these values into the quadratic formula:
$x = \frac{-(5) \pm \sqrt{(5)^2 - 4(2)(-3)}}{2(2)}$
$x = \frac{-5 \pm \sqrt{25 - (-24)}}{4}$
$x = \frac{-5 \pm \sqrt{25 + 24}}{4}$
$x = \frac{-5 \pm \sqrt{49}}{4}$
$x = \frac{-5 \pm 7}{4}$

Now, we calculate the two possible solutions:

Solution 1:
$x_1 = \frac{-5 + 7}{4}$
$x_1 = \frac{2}{4}$
$x_1 = \frac{1}{2}$

Solution 2:
$x_2 = \frac{-5 - 7}{4}$
$x_2 = \frac{-12}{4}$
$x_2 = -3$

The solutions to the equation $2x^2 + 5x - 3 = 0$ are $x = \frac{1}{2}$ and $x = -3$.