Find the Discriminant 5x^2-49x+421=x^2+7x-3

$5 x^{2} - 49 x + 421 = x^{2} + 7 x - 3$

Step 1

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

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

Subtract $x^{2}$ from both sides of the equation.

$5 x^{2} - 49 x + 421 - x^{2} = 7 x - 3$

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

$5 x^{2} - 49 x + 421 - x^{2} - 7 x = - 3$

Add $3$ to both sides of the equation.

$5 x^{2} - 49 x + 421 - x^{2} - 7 x + 3 = 0$

Simplify $5 x^{2} - 49 x + 421 - x^{2} - 7 x + 3$ .

Subtract $x^{2}$ from $5 x^{2}$ .

$4 x^{2} - 49 x + 421 - 7 x + 3 = 0$

Subtract $7 x$ from $- 49 x$ .

$4 x^{2} - 56 x + 421 + 3 = 0$

Add $421$ and $3$ .

$4 x^{2} - 56 x + 424 = 0$

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 $c$ .

${(- 56)}^{2} - 4 (4 \cdot 424)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

Raise $- 56$ to the power of $2$ .

$3136 - 4 (4 \cdot 424)$

Multiply $- 4 (4 \cdot 424)$ .

Multiply $4$ by $424$ .

$3136 - 4 \cdot 1696$

Multiply $- 4$ by $1696$ .

$3136 - 6784$

Subtract $6784$ from $3136$ .

$- 3648$