Solve 3x-5/x=14

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The equation 3x-5/x=14 has to be solved for x.

3x-5/x=14

=> 3x^2 - 5 = 14x

=> 3x^2 - 14x - 5 = 0

=> 3x^2 - 15x + x - 5 = 0

=> 3x(x - 5) + 1(x - 5) = 0

=> (3x + 1)(x - 5) = 0

=> x = -1/3, x = 5

The solution of the equation 3x-5/x=14 is {-1/3, 5}

baxthum8's profile pic

baxthum8 | High School Teacher | (Level 3) Associate Educator

Posted on

Solve `3x - 5/x = 14`

First multiply every term by x to help eliminate the denominator.

`x(3x) - x(5/x) = 14 (x)`

`3x^2 - 5 = 14x` This is a quadratic.  In order to solve, set equal to zero.

`3x^2 - 14x - 5 = 0` Now we could either factor or use quadratic formula to solve.

In factoring this gives us:  `(3x +1) (x - 5) = 0`

Using zero product property we set each factor equal to zero.

`3x + 1 = 0` and `x - 5 = 0`

Solve for x and x is:  `x = -1/3 and x = 5`

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