Linear algebra: What is the value of x if "1/2 + 2/5x = x - 3/4"

Question

Solve for x:

1/2 + 2/5x = x - 3/4

Answer 1

Assuming the problem is 1/2+2/(5*x)=x-3/4
multiply both sides by x
x/2+2/5=x^2-3*x/4 collecting like terms x^2-5*x/4-2/5=0............(1)
solving the quadratic
x=5/8+sqrt(25/64+2/5) and x=5/8-sqrt(25/64+2/5)
solution gives x=1.********** and x=-0.**********
when these values are substituted into equation (1) in turn both result in zero.

If the problem is x/2-2*x/5=x-3/4 it is linear equation resulting in x=25/12

Comments

Interesting how there can be 2 solutions, especially the one involving a quadratic equation.  But it all depends on how a problem (whether it's math, engineering, or product development) is interpreted.  And to observe things from a different point of view is what drives innovation and progress.

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thank you sir

Answer 2

By multiplying x on both LHS and RHS
The equation can be brought to ax^2 + bx + c = 0 form
Then
x = (5/8) + (1/8)*sqrt(23*11/5) & (5/8) - (1/8)*sqrt(23*11/5)

Comments

x = 25/12
Taken from Kahn Academy:
 https://www.khanacademy.org/mission/sat/tasks/5121625989120000

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Don't know what went wrong then !!! My bad LOL :D

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Is that (2/5)*x by any chance?

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The answer here is for
(1/2) + (2/5x) = x - (3/4)

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Should have used brackets to avoid confusion .

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Yes, I see what you mean.  But I took it directly from Kahn Academy, Question #5,
and there were no brackets.

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No worries ! :D