Solve linear equation: x - 15/x = x/3 + 14

x - 15/x = x/3 + 14
Transpose x/3 to LHS and 15/x to RHS
x - x/3 = 14 + 15/x,
LHS → x - x/3 → LCM → 3
(3x - x)/3 = 2x/3 (i)
RHS → 14 + 15/x, LCM = x
(14x + 15)/x (2)
Equate (1) and (2)
2x/3 = (14x + 15)/x
Multiply both sides by 3x
We will get
2x/3 * 3x = (14x + 15)/x * 3x
2x² = 3(14x + 15)
2x² = 42x + 45
2x² - 42x - 45 = 0
Using quadratic formula:
x = (-b ± √(b² - 4ac))/2a
where a = 2, b = -42, c = -45
x = (42 ± √((-42)² - 4 * 2 * -45))/2*2
x = (42 ± √(1764 + 360))/4
x = (42 ± √2124)/4
x = (42 ± 46.087)/4
x = (42 + 46.087)/4 or x = (42 - 46.087)/4
x = 88.087/4 or x = -4.087/4
x = 22.02 or x = -1.02