Find the Discriminant 2x^2=6x+4

$2 x^{2} = 6 x + 4$

Step 1

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

Subtract $6 x$ from both sides of the equation.

$2 x^{2} - 6 x = 4$

Subtract $4$ from both sides of the equation.

$2 x^{2} - 6 x - 4 = 0$

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 $c$ .

${(- 6)}^{2} - 4 (2 \cdot - 4)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

Raise $- 6$ to the power of $2$ .

$36 - 4 (2 \cdot - 4)$

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

Multiply $2$ by $- 4$ .

$36 - 4 \cdot - 8$

Multiply $- 4$ by $- 8$ .

$36 + 32$

Add $36$ and $32$ .

$68$