Question

X(2x-5) = 12 How to solve for x?

Answer 1

Answer:

$x=4,\:x=-\frac{3}{2}$

Step-by-step 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.
$x_{1,\:2}=\frac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4\cdot \:2\left(-12\right)}}{2\cdot \:2}$
$x_{1,\:2}=\frac{-\left(-5\right)\pm \:11}{2\cdot \:2}$
Separate the solutions.
$x_1=\frac{-\left(-5\right)+11}{2\cdot \:2},\:x_2=\frac{-\left(-5\right)-11}{2\cdot \:2}$
Simplify.
$x=4,\:x=-\frac{3}{2}$