quality, equality

Quality or quality means a characteristic or attribute--
He never gets annoyed; that's his most unusual quality.
This place has a strange, moody quality, especially when it rains.

Quality also means character or nature--
"The quality of mercy is not strained..."
Art has the quailty of being timeless; popular culture is ephemeral.

Quality is also used to mean excellence or superiority--
The shop clerk dreamed of becoming a lady of quality, like the heroine of a romance novel.
Bring this to the attention of the quality control manager.

Equality or equality means the state of being alike or the same--
The scale will help to ensure equality of weight.

Equality, when used to refer to persons, means the same or alike in rank, status, or degree--
"Equality under the law shall not be denied or abridged by the United States or by any State on account of sex..."
CORE is an acronym for "Congress of Racial Equality".

Now that you know that, you can say--
"Fairness is his best quality; he really believes in equality for everyone."

Note--"equity" means fairness or impartiality, most commonly as applied to civil suits--
"The judicial Power shall extend to all cases, in Law and Equity, arising under this Constitution..."

Equity may also mean the interest of a stockholder in the corporation--
His equity still doesn't amount to 20%; he can't arrange a takeover.

Equity may also mean the interest of an owner of mortgaged property in the house or land; the amount of it that this person actually owns--
They can't borrow any more money; they only have $10,000 in equity.