Quadratic Equation Calculator

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