Progressive Tax Calculation Formula In Reverse

I came across the solution to this post - [URL] ..... - and was just wondering how to adjust the formula so that it calculates the correct tax starting from the net amount.

Say for example, an employee is paid a fixed, after-tax salary amount, and the employer is responsible for covering the tax - the salary payment needs to be "grossed-up" to calculate the correct amount of tax.

With 'tax brackets' as follows:

Taxable incomeTax on income (2011 – 2012)Tax rate
$0 – $6,000Nil0%
$6,001 – $37,00015c for each $1 over $6,00015%
$37,001 – $80,000$4,650 plus 30c for each $1 over $37,00030%
$80,001 – $180,000$17,550 plus 37c for each $1 over $80,00037%
Over $180,000$54,550 plus 45c for each $1 over $180,00045%

The formula to calculate tax, starting from the gross amount, is:

[Code] ......