Question
$$3(x^2+4)^2-19(x^2+4)-14 = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 3(x^2+4)^2-19(x^2+4)-14 &= 0&& \text{simplify left side} \\[1 em]3(x^4+8x^2+16)-19(x^2+4)-14 &= 0&& \\[1 em]3x^4+24x^2+48-(19x^2+76)-14 &= 0&& \\[1 em]3x^4+24x^2+48-19x^2-76-14 &= 0&& \\[1 em]3x^4+5x^2-42 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
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Equations Solver