How does capital gains impact earned income tax bracket?

Long term capital gains have no affect on the tax rates used to determine taxes on your other taxable income. The capital gains are added to your other taxable income to determine what capital gains tax rates will be applied to the gains. 

If you real question is: how does capital gains impact the Earned income credit (EIC):

The earned income credit is first calculated (actually looked up in a table) on your earned income then it is calculated on your total income (AGI), which includes capital gains. You get the lesser of the two calculated EIC numbers. See the 2018 EIC table at:

https://www.irs.gov/pub/irs-pdf/p596.pdf

 The basic EIC works on a "bell curve," rising as a worker's wages rise reaching a maximum when annual earnings are between $14,000 and $18,350 (Single with 2 or 3 children 2018) and then declining gradually until it phases out altogether. If your income is on the up slope of the EIC curve,  capital gains will not affect your EIC. But if your income is on the down slope, more income (of any kind) will reduce you EIC.