# Irrational Equation A4

Source: algebrica.org - CC BY-NC 4.0
https://algebrica.org/exercises/irrational-equation-a-4/
Fetched from algebrica.org test 14697; source modified 2025-04-25T17:07:54.

Before you begin, review the key concepts behind [irrational equations](../irrational-equations.md) 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}
\\]