Question

3x-5/x=-12 I do not know what to do and how to solve this

Answer 1

To solve the equation 3x-5/x=-12, you need to clear the fraction and solve the resulting quadratic equation using the quadratic formula.

Step-by-step explanation:

To solve the equation 3x-5/x=-12, we need to clear the fraction. Multiply both sides of the equation by x to get rid of the denominator:

3x^2 - 5 = -12x

Rewrite the equation in standard form:

3x^2 + 12x - 5 = 0

Now, we can solve the quadratic equation using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

Plugging in the values a = 3, b = 12, and c = -5, we get:

x = (-12 ± sqrt(12^2 - 4(3)(-5))) / 2(3)

Simplifying further gives us:

x = (-12 ± sqrt(144 + 60)) / 6

x = (-12 ± sqrt(204)) / 6

Now, we can simplify the square root:

x = (-12 ± sqrt(4 * 51)) / 6

x = (-12 ± 2sqrt(51)) / 6

Finally, we can simplify the expression:

x = -2 ± sqrt(51) / 3