Question

`s = (px)/d (d/2 - x)` Make `x` the subject of formula..?

Answer 1

`x = (-pd +- sqrt( (-pd)^2 - 16psd))/(4p)`

Explanation:

For starters, notice that your original equation can be simplified to

`s = (px)/color(red)(cancel(color(black)(d))) * color(red)(cancel(color(black)(d)))/2 - (px)/d * x`

`s = (px)/2 - (px^2)/d`

with `d !=0`.

The fractions present on the right side of the equation have `2d` as the common denominator, so rewrite the equation as

`s = (px)/2 * d/d - (px^2)/d * 2/2`

`s = (pxd - 2px^2)/(2d)`

Multiply both sides by `2d` to get

`2sd = pdx - 2px^2`

Rearrange the equation to quadratic form

`2px^2 - pdx + 2sd = 0`

At this point, you can use the quadratic formula to make `x` the subject of the equation. You know that for a general-form quadratic equation

`color(blue)(ax^2 + bx + c = 0 )`

the quadratic formula looks like this

`color(blue)(x_(1,2) = (-b +- sqrt(b^2 - 4ac))/(2a)`

In your case, you have

• `a = 2p`
• `b = -pd`
• `c = 2sd`

This means that `x` will be

`x = (-(-pd) +- sqrt( (-pd)^2 - 4 * 2p * 2sd))/(2 * 2p)`

`x = (pd +- sqrt( (-pd)^2 - 16psd))/(4p)`

with `p !=0`.