Final answer:
The polynomial equation given has a degree of 5, indicating that there can be up to 5 solutions for the equation, as per the Fundamental Theorem of Algebra.
Step-by-step explanation:
The equation provided (9)/(20) x⁵+3x²-4x+120 is a polynomial equation, not a quadratic equation. To determine the total possible solutions for a polynomial equation, we look at the highest degree of the variable, which is known as the degree of the polynomial. In this case, the highest degree is 5 from the term x⁵, which means there can be up to 5 solutions for this equation. This is based on the Fundamental Theorem of Algebra, which states that every non-zero, single-variable, degree-n polynomial with complex coefficients has counted with multiplicity, exactly n roots/solutions in the complex number system.