Problem: Whats 3x-2 over 9 equals 25 over 3x-2?
(3x - 2)/9 = 25/(3x - 2)
(3x - 2) * ((3x - 2)/9) = (25/(3x - 2)) * (3x - 2)
((3x - 2)^2)/9 = 25
9 * ((3x - 2)^2)/9 = 25 * 9
(3x - 2)^2 = 225
(3x - 2)(3x - 2) = 225
9x^2 - 6x - 6x + 4 = 225
9x^2 - 12x + 4 = 225
9x^2 - 12x + 4 - 225 = 225 - 225
9x^2 - 12x - 221 = 0
Use the quadratic equation to solve.
-b ± sqrt(b² - 4*a*c)
x = ----------------------------
2a
-(-12) ± sqrt(-12² - 4*9*(-221))
x = -----------------------------------------
2(9)
12 ± sqrt(144 + 7956)
x = -------------------------------
18
12 ± sqrt(8100)
x = ----------------------
18
12 ± 90
x = ------------
18
12 + 90 12 - 90
x = ------------ and x = ------------
18 18
102 -78
x = ------- and x = -------
18 18
102 -78
x = ------- and x = -------
18 18
x = 5.66666 and x = -4.33333