Subject of the Formula?

Question

Hi can anyone please show me the steps required to make x the subject of the formula ,any help would be gladly appreciated,thnks

x-y/x=a

Answer 1

YOU DO NOT NEED TO CONFUSE YOURSELF WITH QUADRATIC EQUATIONS IN THIS CASE
[ You cannot have two variables (x and y) in a quadratic equation!]

Your formula:

{x-y}/x = a

Rearrange terms:

a = { x - y } / x [Eq 1:]

Multiply both sides by x ['Removing it' from RHS]

ax = {y - x} [Eq 2:]

Add x to both sides [ 'Removing it' from RHS]

ax + x = y [Eq 3:]

Factorise [Eq 3:] x{a + 1} = y

'Remove' {a + 1} from LHS by dividing both sides by {a + 1} and rearrange terms

x = y / {a + 1} [Eq 4:]


(QED)

[Quad Erat Demonstrandum -- That that was to be Demonstrated]


I have taken liberty with some 'shortcuts' as I went from step to step

But the KEY rules are DO the SAME to BOTH SIDES of AN EQUATION or a Formula! :-)

Answer 2

x-(y/x)=a
multiply both sides by x:
x^2-y=ax
move the ax to the left hand side:
x^2-ax-y=0, now use the quadratic formula to solve for x. This only works if a and y are constants.

Answer 3

The second answerer is correct

Answer 4

x^2-ax-y=0 so x=((a+-sqrt(a^2+4y))/2