Solve 2x² + 5x − 3 = 0 and show each step

The given quadratic equation is in the standard form $ax^2 + bx + c = 0$.
Comparing $2x^2 + 5x - 3 = 0$ with the standard form, we have:
$a = 2$
$b = 5$
$c = -3$

The quadratic formula is:
$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

$x = \frac{-(5) \pm \sqrt{(5)^2 - 4(2)(-3)}}{2(2)}$

Calculate $b^2$:
$5^2 = 25$
Calculate $4ac$:
$4(2)(-3) = 8(-3) = -24$
Calculate $b^2 - 4ac$:
$25 - (-24) = 25 + 24 = 49$

$x = \frac{-5 \pm \sqrt{49}}{4}$

$\sqrt{49} = 7$

$x = \frac{-5 \pm 7}{4}$

For the '+' sign:
$x_1 = \frac{-5 + 7}{4}$
$x_1 = \frac{2}{4}$
$x_1 = \frac{1}{2}$

For the '-' sign:
$x_2 = \frac{-5 - 7}{4}$
$x_2 = \frac{-12}{4}$
$x_2 = -3$

Thus, the solutions are $x = \frac{1}{2}$ and $x = -3$.