Find the Discriminant 0=-2x^2+6x+13

$0 = - 2 x^{2} + 6 x + 13$

Step 1

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

Add $2 x^{2}$ to both sides of the equation.

$2 x^{2} = 6 x + 13$

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

$2 x^{2} - 6 x = 13$

Subtract $13$ from both sides of the equation.

$2 x^{2} - 6 x - 13 = 0$

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 $c$ .

${(- 6)}^{2} - 4 (2 \cdot - 13)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

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

$36 - 4 (2 \cdot - 13)$

Multiply $- 4 (2 \cdot - 13)$ .

Multiply $2$ by $- 13$ .

$36 - 4 \cdot - 26$

Multiply $- 4$ by $- 26$ .

$36 + 104$

Add $36$ and $104$ .

$140$