Find the Discriminant 4x^2+107x+313=-x^2+7x-7

$4 x^{2} + 107 x + 313 = - x^{2} + 7 x - 7$

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

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

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

$4 x^{2} + 107 x + 313 + x^{2} = 7 x - 7$

Subtract $7 x$ from both sides of the equation.

$4 x^{2} + 107 x + 313 + x^{2} - 7 x = - 7$

Add $7$ to both sides of the equation.

$4 x^{2} + 107 x + 313 + x^{2} - 7 x + 7 = 0$

Simplify $4 x^{2} + 107 x + 313 + x^{2} - 7 x + 7$ .

Add $4 x^{2}$ and $x^{2}$ .

$5 x^{2} + 107 x + 313 - 7 x + 7 = 0$

Subtract $7 x$ from $107 x$ .

$5 x^{2} + 100 x + 313 + 7 = 0$

Add $313$ and $7$ .

$5 x^{2} + 100 x + 320 = 0$

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 $c$ .

$100^{2} - 4 (5 \cdot 320)$

Evaluate the result to find the discriminant.

Simplify each term.

Raise $100$ to the power of $2$ .

$10000 - 4 (5 \cdot 320)$

Multiply $5$ by $320$ .

$10000 - 4 \cdot 1600$

Multiply $- 4$ by $1600$ .

$10000 - 6400$

Subtract $6400$ from $10000$ .

$3600$