How do you find the solution to the quadratic equation # 4x^3 + 12x^2 - 26x - 24 = 0#?
A quadratic equation can be put in the form
This is not a quadratic, it is a cubic equation.
If you know the rational zeros theorem, you can try to find a rationahl solution. (There is none.)
If you know calculus and Newton's method, you can approximate the solutions to any desired degree of accuracy.
If you know the cubic formula (no one on our faculty where I teach has it memorized) , then you can use it to write the solutions using square roots and cube roots.
Or, you can use technology.