To solve the ten cubic equations *with* the quadratic term, this term has to be removed by transforming it into a linear term, and the transformed equation then can be solved by the formula of Scipione dal Ferro and Tartaglia, which today is unjustly called *Cardano's formula* because he was the first to publish it, in his *Ars magna* in 1545.

Tartaglia did not find a way to solve the ten cubic equations with the quadratic term. It is true that he printed the solution of the equation .1.*cubo piu* .6.*censi equal à* .100. (*x*^{3}+6*x*^{2}=100) in his book *Quesiti et inventioni diverse* (*Diverse problems and inventions*) of 1546, but this example was plagiarized from Chapter XV of Cardano's *Ars magna* of 1545, and he even introduced an error.

Cardano gave the solution in Latin:

R*V:cubica* 42 *p*:R 1700 *p*:R*V:cubica* 42 *m*:R 1700 *m*:2,

where *V* is the abbreviation of *Vniversalis, p:* means plus, and *m:* minus. Therefore, the root in modern notation is \[ {\sqrt[3]{42+\sqrt{1700}}}+{\sqrt[3]{42-\sqrt{1700}}}-2\,\,(=3.282260\dots).\]

^{ }

But Tartaglia's solution

R.*u.cu*.42.*piu* R.17000. *piu* R.*u.cu*.42.*men*.R.17000.*men*.2.

twice has 17000 instead of the correct 1700.

Scipione dal Ferro and Nicolo Tartaglia found the solution of the three cubic equations *without* a quadratic term.

*But it was Cardano's great immortal feat to have solved the other ten cubic equations with a quadratic term, and thus to lead the way to a general solution.*