Before you begin, review the key concepts behind irrational equations to better follow the solution process.

Solve the irrational equation

\[\sqrt{3x^2-8x} = -5 \]

The solution is immediate and requires no computation. The equation is of the form: \[ \sqrt[n]{f(x)} = k \]

where \( k \) is a negative real number and \( n \) is even. Since even-indexed roots of real numbers are always non-negative, the equation has no real solution.

Solution \[\not \exists\; x \in \mathbb{R}\]