Question

Solve 2x^2 - 3x = 12 using the quadratic formula.

Answer 1

Answer:

$x = \frac{3}{4} + \frac{ \sqrt{105} }{4} \: \: , \: \: \: x = \frac{3}{4} - \frac{ \sqrt{105} }{4}$

Step-by-step explanation:

2x² - 3x - 12 = 0

Using the quadratic formula which is

$x = \frac{ - b \pm\sqrt{ {b}^{2} - 4ac} }{2a}$

From the question

a = 2 , b = - 3 , c = - 12

So we have

$x = \frac{ - - 3\pm \sqrt{ ({ - 3})^{2} - 4(2)( - 12)} }{2(2)} \\ = \frac{3\pm \sqrt{9 + 96} }{4} \\ = \frac{3\pm \sqrt{105} }{4} \: \: \: \: \: \:$

Separate the solutions

We have the final answer as

$x = \frac{3}{4} + \frac{ \sqrt{105} }{4} \: \: , \: \: \: x = \frac{3}{4} - \frac{ \sqrt{105} }{4}$

Hope this helps you