Answer:
x = 18
Step-by-step explanation:
Since both right triangles are similar, therefore:
[tex] \frac{2x - 6}{20} = \frac{39}{x + 8} [/tex]
Cross multiply
[tex] (2x - 6)(x + 8) = 39*20 [/tex]
[tex] 2x(x + 8) -6(x + 8) = 780 [/tex]
[tex] 2x^2 + 16x - 6x - 48 = 780 [/tex]
[tex] 2x^2 + 10x - 48 = 780 [/tex]
Subtract 780 from both sides
[tex] 2x^2 + 10x - 48 - 780 = 0 [/tex]
[tex] 2x^2 + 10x - 828 = 0 [/tex]
[tex] 2x^2 + 46x - 36x - 828 = 0 [/tex]
[tex] 2x(x + 23) - 36(x + 23) = 0 [/tex]
[tex] (x + 23)(2x - 36) = 0 [/tex]
x + 23 = 0
x = -23
Or
2x - 36 = 0
2x = 36
x = 18
