Question

Solve the equation 6w2 – 7w – 20 = 0.

Answer 1

ANSWER


`{w} = (5)/(2)\: or \: w = - (4)/(3)`

Step-by-step explanation

We want to solve the equation:


`6 {w}^(2) - 7w - 20 = 0`

Let us use the method of factorization

Split the middle term;


`6 {w}^(2) -1 5w + 8w- 20 = 0`

Factor by grouping:


`3w( {w} - 5)w + 4(2w- 5) = 0`

Factor further,


`( {2w} - 5)(3w + 4) = 0`

Use the zero product principle.


`( {2w} - 5) = 0 \: or \: (3w + 4) = 0`


`{2w} = 5\: or \: 3w = - 4`

The solution is:


`{w} = (5)/(2)\: or \: w = - (4)/(3)`

Answer 2

For this case we have the following quadratic equation:

`6w ^ 2-7w-20 = 0`

Where:

`a = 6\\b = -7\\c = -20`

Its roots will be given by:

`w = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}\\w = \frac {- (- 7) \pm \sqrt {(- 7) ^ 2-4 (6) (- 20)}} {2 (6)}\\w = \frac {7 \pm \sqrt {49 + 480}} {12}\\w = \frac {7 \pm \sqrt {529}} {12}\\w = \frac {7 \pm23} {12}`

The roots are:

`w_ {1} = \frac {7 + 23} {12} = \frac {30} {12} = \frac {15} {6} = \frac {5} {2}\\w_ {2} = \frac {7-23} {12} = \frac {-16} {12} = - \frac {8} {6} = - \frac {4} {3}`

Answer:

`w_ {1} = \frac {5} {2}\\w_ {2} = - \frac {4} {3}`