Solve please

Step 1: Identify the equation to be solved. The equation is $2x^2 + 5x - 3 = 0$.

Step 2: Use the quadratic formula to solve for $x$. The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. In this equation, $a=2$, $b=5$, and $c=-3$.

Step 3: Substitute the values of $a$, $b$, and $c$ into the quadratic formula. $x = \frac{-5 \pm \sqrt{5^2 - 4(2)(-3)}}{2(2)}$

Step 4: Simplify the expression under the square root. $x = \frac{-5 \pm \sqrt{25 - (-24)}}{4}$ $x = \frac{-5 \pm \sqrt{25 + 24}}{4}$ $x = \frac{-5 \pm \sqrt{49}}{4}$

Step 5: Calculate the square root. $x = \frac{-5 \pm 7}{4}$

Step 6: Solve for the two possible values of $x$. For the '+' case: $x_1 = \frac{-5 + 7}{4} = \frac{2}{4} = \frac{1}{2}$ For the '-' case: $x_2 = \frac{-5 - 7}{4} = \frac{-12}{4} = -3$

The solutions are $x = \frac{1}{2}$ and $x = -3$.

x = \frac{1{2}, x = -3}