Solution set of inequality?

Question

Please help, I can't figure this problem out. I've been working at it for quite awhile.

x^2 -7x - 12 < 0

I came out with (7 + √97)/2 and (7 - √97)/2

Additional Details

I used the quadratic formula

Answer 1

x^2 -7x - 12 < 0

x²-7x-12<0

Now slove the eqations is factor method

Formula  x =  [- b+ √( b²-4ac)]/2a

x²-7x-12<0

here a = 1 , b = - 7 and c = - 12

a , b and c value substitute above formula

x =  [ -(-7)+ √( (-7)²-4(1)(-12) ) ] / 2(1)

Simplfy

 x < [ 7 + √( (49) +48 ) ] / 2

x < [ 7 + √(97) ] / 2

There fore x < [ 7 + √(97)] / 2  or  x < [ 7 - √(97)]

Comments

Solution of the inequality is .

Answer 2

The inequality is

Related equation is

Compare it to quadratic equation

Roots are

Now, there are two ways this product could be less than zero.One factor must be negative and one must be positive.

First situation:

There are NO values for which this situation is true.

Second situation:

This tells you that

Solution