Find the Discriminant 2x^2=4x+3

$2 x^{2} = 4 x + 3$

Step 1

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

Subtract $4 x$ from both sides of the equation.

$2 x^{2} - 4 x = 3$

Subtract $3$ from both sides of the equation.

$2 x^{2} - 4 x - 3 = 0$

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 $c$ .

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

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

Raise $- 4$ to the power of $2$ .

$16 - 4 (2 \cdot - 3)$

Multiply $- 4 (2 \cdot - 3)$ .

Multiply $2$ by $- 3$ .

$16 - 4 \cdot - 6$

Multiply $- 4$ by $- 6$ .

$16 + 24$

Add $16$ and $24$ .

$40$