Question

X(2x-5) = 12

How to solve for x?

Answer 1

`x=4,\:x=-(3)/(2)`

Explanation:

`x\left(2x-5\right)`

Apply the distributive law.


`=x\cdot \:2x-x\cdot \:5`

`=2x^2-5x`

`2x^2-5x=12`
Subtract 12 from both sides.

`2x^2-5x-12=12-12`

`2x^2-5x-12=0`
Now, apply the quadratic formula.

`x_(1,\:2)=(-\left(-5\right)\pm √(\left(-5\right)^2-4\cdot \:2\left(-12\right)))/(2\cdot \:2)`

`x_(1,\:2)=(-\left(-5\right)\pm \:11)/(2\cdot \:2)`
Separate the solutions.

`x_1=(-\left(-5\right)+11)/(2\cdot \:2),\:x_2=(-\left(-5\right)-11)/(2\cdot \:2)`
Simplify.

`x=4,\:x=-(3)/(2)`