Answer:
x = [tex]\frac{4}{5},5[/tex]
Step-by-step explanation:
If both the triangles ΔABC and ΔBCD are congruent,
Corresponding sides of both the triangles will be proportional.
[tex]\frac{AB}{BD}=\frac{AC}{CD}[/tex]
[tex]\frac{5x}{3x+10}=\frac{5x-2}{4x+3}[/tex]
5x(4x + 3) = (5x - 2)(3x + 10)
20x² + 15x = 15x² + 50x - 6x - 20
20x² + 15x = 15x² + 44x - 20
20x² - 15x² = 44x - 15x - 20
5x² = 29x - 20
5x² - 29x + 20 = 0
5x² - 25x - 4x + 20 = 0
5x(x - 5) - 4(x - 5) = 0
(5x - 4)(x - 5) = 0
[tex]x=\frac{4}{5},5[/tex]
