Answer:
x = 3 ± √(39)
Explanation:
x 6
----- = -------
(x+5) x
We can solve using cross products
x * x = 6(x+5)
x^2 = 6x+30
Subtract 6x from each side
x^2 -6x= 6x+30-6x
x^2 -6x= 30
Subtract 30 from each side
x^2 -6x -30 = 30-30
x^2 -6x -30 =0
Using the quadratic formula
x = -b ± √(b^2 -4ac)
-------------------------
2a
where a=1 b = -6 and c = -30
x = -(-6) ± √((-6)^2 -4(1)(-30))
-------------------------
2(1)
x = 6 ± √(36 +120)
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2
x = 6 ± √(156)
-------------------------
2
x = 6 ± √(4*39)
-------------------------
2
x = 6 ± 2√(39)
-------------------------
2
x = 3 ± √(39)