Find the Discriminant -6x^2-2x+77=-7x^2+6x+3

$- 6 x^{2} - 2 x + 77 = - 7 x^{2} + 6 x + 3$

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.

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

$- 6 x^{2} - 2 x + 77 + 7 x^{2} = 6 x + 3$

Subtract $6 x$ from both sides of the equation.

$- 6 x^{2} - 2 x + 77 + 7 x^{2} - 6 x = 3$

Subtract $3$ from both sides of the equation.

$- 6 x^{2} - 2 x + 77 + 7 x^{2} - 6 x - 3 = 0$

Simplify $- 6 x^{2} - 2 x + 77 + 7 x^{2} - 6 x - 3$ .

Add $- 6 x^{2}$ and $7 x^{2}$ .

$x^{2} - 2 x + 77 - 6 x - 3 = 0$

Subtract $6 x$ from $- 2 x$ .

$x^{2} - 8 x + 77 - 3 = 0$

Subtract $3$ from $77$ .

$x^{2} - 8 x + 74 = 0$

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 $c$ .

${(- 8)}^{2} - 4 (1 \cdot 74)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

Raise $- 8$ to the power of $2$ .

$64 - 4 (1 \cdot 74)$

Multiply $- 4 (1 \cdot 74)$ .

Multiply $74$ by $1$ .

$64 - 4 \cdot 74$

Multiply $- 4$ by $74$ .

$64 - 296$

Subtract $296$ from $64$ .

$- 232$