X-3/x=3/5
x - 3/x = 3/5.
Multiply Eq by 5x:
5x^2 - 15 = 3x.
5x^2 - 3x -15 = 0.
Use Quad. Formula.
X = -1.46, and 2.06.
If you mean:
(x-3)/x = 3/5.
Multiply Eq by 5x:
5x-15 = 3x.
5x - 3x = 15.
2x = 15.
X = 7.5.
To solve the equation X - 3/x = 3/5, you can follow these steps:
Step 1: Clear the fraction by multiplying both sides of the equation by 5x (the least common multiple of denominators 1 and 5):
5x(X - 3/x) = 5x(3/5)
This becomes:
5x(X) - 5x(3/x) = 3x
Step 2: Distribute the multiplication on both sides:
5x^2 - 15 = 3x
Step 3: Move all the terms to one side of the equation by subtracting 3x from both sides:
5x^2 - 3x - 15 = 0
Step 4: Rearrange the equation in standard quadratic form by moving all terms to one side:
5x^2 - 3x - 15 = 0
Step 5: Solve the quadratic equation. If the equation does not easily factor, you can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 5, b = -3, and c = -15. Substitute these values into the formula:
x = (-(-3) ± √((-3)^2 - 4 * 5 * (-15))) / (2 * 5)
Simplifying further:
x = (3 ± √(9 + 300)) / 10
x = (3 ± √309) / 10
Therefore, the solutions to the equation are:
x = (3 + √309) / 10 and x = (3 - √309) / 10