Name: Discriminant and number of solutions: solution walkthrough
Uploaded: 2026-11-13
Duration: 1 min 48 s
Description: Which statement describes the real solutions of the equation x² + 6x = 2x - 9? Try it, then watch the animated solution.

First get

0

alone on one side: subtract

2x

and add

9

to get

x^2 + 4x + 9 = 0

.

Solutions are where the graph meets the

x

-axis. The discriminant

b^2 - 4ac

tells how many there are.

Put in

a = 1

,

b = 4

and

c = 9

:

4^2 - 4(1)(9) = 16 - 36 = {-20}

.

The discriminant is negative, so there are no real solutions. The graph never reaches the

x

-axis.

Traps: using

b = 6

gives

0

, using

c = {-9}

gives

52

, and using

b = 8

gives

28

.

Try it first