Quadratic formula is the solution of the quadratic equation. In this method, the roots of a quadratic equation is evaluated by using this direct formula.

For example, $ax^2+bx+c = 0$ is a quadratic equation in standard form and the solution of this quadratic equation is given below.

$x = \dfrac{-b \pm \sqrt{b^2 -4ac}}{2a}$

## Example

$3x^2 + 2x -5 = 0$ is a quadratic equation.

Compare this equation with standard form quadratic equation $ax^2 + bx + c = 0$. Therefore, $a = 3$, $b = 2$ and $c = -5$. Substitute these values in the quadratic formula to obtain the roots.

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

$\implies x = \dfrac{-2 \pm \sqrt{4 + 60}}{6}$

$\implies x = \dfrac{-2 \pm \sqrt{64}}{6}$

$\implies x = \dfrac{-2 \pm 8}{6}$

$\implies x = \dfrac{-2 + 8}{6}$ and $x = \dfrac{-2 -8}{6}$.

$\implies x = \dfrac{6}{6}$ and $x = \dfrac{-10}{6}$.

$\therefore \,\,\, x = 1$ and $x = -\dfrac{5}{3}$.

Using the quadratic formula method, the roots of the quadratic equation $3x^2 + 2x -5 = 0$ are $1$ and $-\dfrac{5}{3}$.