Answer:
x =
, x = 20
Explanation:
2(
) - 5 (
) = 3
Multiply through by (x + 2)(3x - 5) to eliminate the fractions
2(3x - 5)² - 5(x + 2)² = 3(x + 2)(3x - 5) ← expand factors on both sides
2(9x² - 30x + 25) - 5(x² + 4x + 4) = 3(3x² + x - 10) ← distribute parenthesis
18x² - 60x + 50 - 5x² - 20x - 20 = 9x² + 3x - 30 ← simplify left side
13x² - 80x + 30 = 9x² + 3x - 30 ( subtract 9x² + 3x - 30 from both sides )
4x² - 83x + 60 = 0 factor by splitting the x- term
4x² - 80x - 3x + 60 = 0
4x(x - 20) - 3(x - 20) = 0
(4x - 3)(x - 20) = 0
Equate each factor to zero and solve for x
4x - 3 = 0 ⇒ 4x = 3 ⇒ x =
x - 20 = 0 ⇒ x = 20