Answer:
3x-1/4 -1/x = 3(2x+1)/8
x≠0
3x-1/4-1/x = (6x+3)/8
3x-1/4-1/x-(6x+3)/8 = 0
(24x²-2x-8-6x²-3x)/8x=0
24x²-2x-8-6x²-3x=0
18x²-5x-8=0
To solve the quadratic equation 18x² - 5x - 8 = 0, we can use the quadratic formula. The quadratic formula states that for any equation in the form of ax² + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b² - 4ac)) / 2a
Where:
a = 18
b = -5
c = -8
x = (5 ± √((-5)² - 4 * 18 * (-8))) / 2 * 18
x = (5 ± √(25 + 576)) / 36
x = (5 ± √601) / 36
So, the two solutions for x are: x = (5 + √601) / 36
x = (5 - √601) / 36
Explanation: