# Discriminant Calculator

## Calculate the discriminant of a quadratic equation step by step

The calculator will find the discriminant of the given quadratic equation, with steps shown.

Related calculator: Quadratic Equation Calculator

### Your Input

**Find the discriminant of $$$3 x^{2} - 4 x + 5 = 0$$$.**

### Solution

The discriminant of the quadratic equation $$$a x^{2} + b x + c$$$ is $$$D = b^{2} - 4 a c$$$.

Our equation is $$$3 x^{2} - 4 x + 5 = 0$$$, so $$$a = 3$$$, $$$b = -4$$$, $$$c = 5$$$.

Thus, $$$D = \left(-4\right)^{2} - \left(4\right)\cdot \left(3\right)\cdot \left(5\right) = -44$$$.