Find the Discriminant 6x^2+21x=5x^2+7x

$6 x^{2} + 21 x = 5 x^{2} + 7 x$

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

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

Subtract $5 x^{2}$ from both sides of the equation.

$6 x^{2} + 21 x - 5 x^{2} = 7 x$

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

$6 x^{2} + 21 x - 5 x^{2} - 7 x = 0$

Simplify $6 x^{2} + 21 x - 5 x^{2} - 7 x$ .

Subtract $5 x^{2}$ from $6 x^{2}$ .

$x^{2} + 21 x - 7 x = 0$

Subtract $7 x$ from $21 x$ .

$x^{2} + 14 x = 0$

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 $c$ .

$14^{2} - 4 (1 \cdot 0)$

Evaluate the result to find the discriminant.

Simplify each term.

Raise $14$ to the power of $2$ .

$196 - 4 (1 \cdot 0)$

Multiply $0$ by $1$ .

$196 - 4 \cdot 0$

Multiply $- 4$ by $0$ .

$196 + 0$

Add $196$ and $0$ .

$196$