Find the Discriminant 2x^2=16x-32

$2 x^{2} = 16 x - 32$

Step 1

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

Subtract $16 x$ from both sides of the equation.

$2 x^{2} - 16 x = - 32$

Add $32$ to both sides of the equation.

$2 x^{2} - 16 x + 32 = 0$

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 $c$ .

${(- 16)}^{2} - 4 (2 \cdot 32)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

Raise $- 16$ to the power of $2$ .

$256 - 4 (2 \cdot 32)$

Multiply $- 4 (2 \cdot 32)$ .

Multiply $2$ by $32$ .

$256 - 4 \cdot 64$

Multiply $- 4$ by $64$ .

$256 - 256$

Subtract $256$ from $256$ .

$0$