Find the Discriminant 3x^2=2x-1

$3 x^{2} = 2 x - 1$

Step 1

Move all the expressions to the left side of the equation.

Subtract $2 x$ from both sides of the equation.

$3 x^{2} - 2 x = - 1$

Add $1$ to both sides of the equation.

$3 x^{2} - 2 x + 1 = 0$

Step 2

The discriminant of a quadratic is the expression inside the radical of the quadratic formula.

$b^{2} - 4 (a c)$

Step 3

Substitute in the values of $a$ , $b$ , and $c$ .

${(- 2)}^{2} - 4 (3 \cdot 1)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

Raise $- 2$ to the power of $2$ .

$4 - 4 (3 \cdot 1)$

Multiply $- 4 (3 \cdot 1)$ .

Multiply $3$ by $1$ .

$4 - 4 \cdot 3$

Multiply $- 4$ by $3$ .

$4 - 12$

Subtract $12$ from $4$ .

$- 8$