# Quadratic Equation Calculator

## Solve quadratic equations step by step

The calculator will solve the quadratic equation step by step either by completing the square or using the quadratic formula. It will find both the real and the imaginary (complex) roots.

Related calculator: Discriminant Calculator

### Solution

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