Questions on Algebra: Complex Numbers answered by real tutors!

You can put this solution on YOUR website!
2/3x-7=x
------------
Multiply by 3x
2 - 21x = 3x^2
3x^2 + 21x - 2 = 0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation ax^2+bx+c=0

(in our case 3x^2+21x+-2 = 0

) has the following solutons:

$x[12] = (b+-sqrt( b^2-4ac ))/2\a$

For these solutions to exist, the discriminant b^2-4ac

should not be a negative number.

First, we need to compute the discriminant b^2-4ac

.

Discriminant d=465 is greater than zero. That means that there are two solutions: $x[12] = (-21+-sqrt( 465 ))/2\a$ .

$x[1] = (-(21)+sqrt( 465 ))/2\3 = 0.0939764421413039$
$x[2] = (-(21)-sqrt( 465 ))/2\3 = -7.0939764421413$

Quadratic expression 3x^2+21x+-2

can be factored:
3x^2+21x+-2 = (x-0.0939764421413039)*(x--7.0939764421413)

Again, the answer is: 0.0939764421413039, -7.0939764421413. Here's your graph:
graph( 500, 500, -10, 10, -20, 20, 3*x^2+21*x+-2 )