There is a general formula for solving quadratic equations, namely the Quadratic Formula:

$$ x = \frac{ -b \pm \sqrt{ b^2 - 4ac } }{ 2a } $$

For third degree equations of the form $ax^3+bx^2+cx+d=0$, there is a set of three equations: one for each root.

Is there a general formula for solving equations of the following form?

$$ ax^4 + bx^3 + cx^2 + dx + e = 0 $$

How about for higher degrees? If not, why not?

There is a general formula for solving quadratic equations, namely the Quadratic Formula, or the Sridharacharya Formula:

$$x = \frac{ -b \pm \sqrt{ b^2 - 4ac } }{ 2a } $$

For cubic equations of the form $ax^3+bx^2+cx+d=0$, there is a set of three equations, one for each root.

Is there a general formula for solving equations of the following form [Quartic Equations]?

$$ ax^4 + bx^3 + cx^2 + dx + e = 0 $$

How about for higher degrees? If not, why not?

There is a general formula for solving quadratic equations, namely the Quadratic Formula.

For third degree equations of the form $ax^3+bx^2+cx+d=0$, there is a set of three equations: one for each root.

Is there a general formula for solving equations of the form $ax^4+bx^3+cx^2+dx+e=0$ ?

How about for higher degrees? If not, why not?

There is a general formula for solving quadratic equations, namely the Quadratic Formula:

$$ x = \frac{ -b \pm \sqrt{ b^2 - 4ac } }{ 2a } $$

For third degree equations of the form $ax^3+bx^2+cx+d=0$, there is a set of three equations: one for each root.

Is there a general formula for solving equations of the following form?

$$ ax^4 + bx^3 + cx^2 + dx + e = 0 $$

How about for higher degrees? If not, why not?