SOLUTION: How would I solve n-10/5=10/n+9

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Question 722641: How would I solve n-10/5=10/n+9
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

%28n-10%29%2F5=10%2F%28n%2B9%29 ...cross multiply
%28n-10%29%28n%2B9%29=10%2A5
n%5E2%2B9n-10n-90=50
n%5E2-n-90-50=0
n%5E2-n-140=0......use quadratic formula to find n

n+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
n+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%2A1%2A%28-140%29+%29%29%2F%282%2A1%29+
n+=+%281+%2B-+sqrt%281%2B560+%29%29%2F2+
n+=+%281+%2B-+sqrt%28561+%29%29%2F2+
n+=+%281+%2B-+23.69%29%2F2+
solutions:
n+=+%281+%2B23.69%29%2F2+
n+=+24.69%2F2+
n+=12.345+
or
n+=+%281+-23.69%29%2F2+
n+=+-22.69%2F2+
n+=-11.345+

check solutions:
%28n-10%29%2F5=10%2F%28n%2B9%29....n+=12.345+
%2812.345-10%29%2F5=10%2F%2812.345%2B9%29
2.345%2F5=10%2F21.345
0.469=0.46849
0.469=0.469

%28n-10%29%2F5=10%2F%28n%2B9%29....n+=-11.345+
%28-11.345-10%29%2F5=10%2F%28-11.345%2B9%29
-21.345%2F5=10%2F-2.345
-4.269=-4.269