Find the Discriminant -40x+28=-4x^2-8x

$- 40 x + 28 = - 4 x^{2} - 8 x$

Move all terms to the left side of the equation and simplify.

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

Add $4 x^{2}$ to both sides of the equation.

$- 40 x + 28 + 4 x^{2} = - 8 x$

Add $8 x$ to both sides of the equation.

$- 40 x + 28 + 4 x^{2} + 8 x = 0$

Add $- 40 x$ and $8 x$ .

$- 32 x + 28 + 4 x^{2} = 0$

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

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

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

${(- 32)}^{2} - 4 (4 \cdot 28)$

Evaluate the result to find the discriminant.

Simplify each term.

Raise $- 32$ to the power of $2$ .

$1024 - 4 (4 \cdot 28)$

Multiply $4$ by $28$ .

$1024 - 4 \cdot 112$

Multiply $- 4$ by $112$ .

$1024 - 448$

Subtract $448$ from $1024$ .

$576$