Analytical solutions of cubic and quartic equations

Curious3141

Even though it is uncommon to see questions asking for an analytical solution to equations of degree 3 or 4, they have been asked on the forum. It's also good to know how, in any case.

Cubic : http://www.karlscalculus.org/cubic.html

Quartic : http://www.karlscalculus.org/quartic.html

For the cubic equation, I would discourage simply memorising the general formula; instead, try to understand the method and remember the form of the required substitutions to reduce the cubic to a quadratic.

IMHO, the cubic is still doable by hand. The quartic is often too tedious to contemplate solving analytically (without a computer), but the method is instructive.