Find the Discriminant 3x(x-2)=x-4

$3 x (x - 2) = x - 4$

Step 1

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

Simplify the left side.

Simplify $3 x (x - 2)$ .

Apply the distributive property.

$3 x \cdot x + 3 x \cdot - 2 = x - 4$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$3 (x \cdot x) + 3 x \cdot - 2 = x - 4$

Multiply $x$ by $x$ .

$3 x^{2} + 3 x \cdot - 2 = x - 4$

Multiply $- 2$ by $3$ .

$3 x^{2} - 6 x = x - 4$

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

Subtract $x$ from both sides of the equation.

$3 x^{2} - 6 x - x = - 4$

Add $4$ to both sides of the equation.

$3 x^{2} - 6 x - x + 4 = 0$

Subtract $x$ from $- 6 x$ .

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

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 $c$ .

${(- 7)}^{2} - 4 (3 \cdot 4)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

Raise $- 7$ to the power of $2$ .

$49 - 4 (3 \cdot 4)$

Multiply $- 4 (3 \cdot 4)$ .

Multiply $3$ by $4$ .

$49 - 4 \cdot 12$

Multiply $- 4$ by $12$ .

$49 - 48$

Subtract $48$ from $49$ .

$1$