Find the solutions to the equation below. 6x^2+5x-4=0

Hi NinjaDevo,

You give great detailed answers along with showing how to check, that is really great.

However think about this step

 6x²+5x-4=0

(3x + 4)(2x - 1) = 0

I think that for many people this is the step that causes the greatest amount of problems and you have not described how you did it.

Here is a you tube clip to show you how to do it.

https://www.youtube.com/watch?v=HvBiJ9W00Z4

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Some times it is easier just to use the quadratic forumla. (right from the beginning)

If you have problems remembering it this clip will help you.

https://www.youtube.com/watch?v=O8ezDEk3qCg

In this case a=6, b=5, c=-4

Find all solutions for x: 6x²+5x-4=0

We can start by factoring this polynomial.

 6x²+5x-4=0

(3x + 4)(2x - 1) = 0

This means that (3x + 4) = 0 and (2x - 1) = 0

Let's start with the first solution for x:

(3x + 4) = 0

-4             -4             ---Subtract 4 from both sides

3x = -4

÷3      ÷3           ---Divide 3 by both sides

x = -4/3

 

And now our second solution:

(2x - 1) = 0

       +1    +1        ---Add 1 to both sides

2x = 1

÷2      ÷2              ---Divide both sides by 2

x = 1/2

 

There we go! Our two solutions for x are: x = 1/2 and x = -4/3.

Check:

6(-4/3)²+5(-4/3)-4=0

6(16/9)+(-20/3)-4 = 0

(96/9)+(-60/9)-4 = 0

36/9 - 4 = 0

4-4 = 0

0=0 ✓

 

6(1/2)²+5(1/2)-4=0

6(1/4)+5/2-4 = 0

1.5 + 2.5-4 = 0

4-4=0

0=0   ✓