Find the Discriminant 6x^2=8x+7

$6 x^{2} = 8 x + 7$

Step 1

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

Subtract $8 x$ from both sides of the equation.

$6 x^{2} - 8 x = 7$

Subtract $7$ from both sides of the equation.

$6 x^{2} - 8 x - 7 = 0$

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 $c$ .

${(- 8)}^{2} - 4 (6 \cdot - 7)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

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

$64 - 4 (6 \cdot - 7)$

Multiply $- 4 (6 \cdot - 7)$ .

Multiply $6$ by $- 7$ .

$64 - 4 \cdot - 42$

Multiply $- 4$ by $- 42$ .

$64 + 168$

Add $64$ and $168$ .

$232$