Find the Discriminant -5x^2+19x+176=-7x^2-x

$- 5 x^{2} + 19 x + 176 = - 7 x^{2} - x$

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

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

Add $7 x^{2}$ to both sides of the equation.

$- 5 x^{2} + 19 x + 176 + 7 x^{2} = - x$

Add $x$ to both sides of the equation.

$- 5 x^{2} + 19 x + 176 + 7 x^{2} + x = 0$

Simplify $- 5 x^{2} + 19 x + 176 + 7 x^{2} + x$ .

Add $- 5 x^{2}$ and $7 x^{2}$ .

$2 x^{2} + 19 x + 176 + x = 0$

Add $19 x$ and $x$ .

$2 x^{2} + 20 x + 176 = 0$

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 $c$ .

$20^{2} - 4 (2 \cdot 176)$

Evaluate the result to find the discriminant.

Simplify each term.

Raise $20$ to the power of $2$ .

$400 - 4 (2 \cdot 176)$

Multiply $2$ by $176$ .

$400 - 4 \cdot 352$

Multiply $- 4$ by $352$ .

$400 - 1408$

Subtract $1408$ from $400$ .

$- 1008$