Answer:
(5 + √115)/15 or (5 - √115)/15
Step-by-step explanation:
4/5x+4/3 = 2x
Multiply each term by the least common multiple of the denominators (15x)
12 + 20x = 30x²
Move all the terms to the left-hand side.
-30x² + 20x + 12 = 0
Multiply each term by -1
30x² - 20x - 12 = 0
Remove the common factor (2)
15x² - 10x - 6 = 0
Solve by using the quadratic formula
a = 15, b = -10, c = -6
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\= \frac{-(-10)\pm\sqrt{(-10)^2-4(15)(-6)}}{2(15)}\\\\= \frac{10\pm\sqrt{100 + 360}}{30}\\\\= \frac{10\pm\sqrt{460}}{30}\\\\= \frac{10\pm\sqrt{4\times115}}{30}\\\\= \frac{10\pm2\sqrt{115}}{30}\\\\= \mathbf{\frac{5\pm\sqrt{115}}{15}}[/tex]
x = (5 + √115)/15 or x = (5 - √115)/15
