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Your input: solve the quadratic equation $$$2 x^{2} + 5 x - 3 = 0$$$ by using quadratic formula.

The standard quadratic equation has the form $$$ax^2+bx+c=0$$$.

In our case, $$$a=2$$$, $$$b=5$$$, $$$c=-3$$$.

Now, find the discriminant using the formula $$$D=b^2-4ac$$$: $$$D=5^2-4\cdot 2 \cdot \left(-3\right)=49$$$.

Find the roots of the equation using the formulas $$$x_1=\frac{-b-\sqrt{D}}{2a}$$$ and $$$x_2=\frac{-b+\sqrt{D}}{2a}$$$

$$$x_1=\frac{-5-\sqrt{49}}{2\cdot 2}=-3$$$ and $$$x_2=\frac{-5+\sqrt{49}}{2\cdot 2}=\frac{1}{2}$$$

Answer: $$$x_1=-3$$$; $$$x_2=\frac{1}{2}$$$