Question
$$(2x^2+3x-1)^2-10x\cdot2-15x+9 = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} (2x^2+3x-1)^2-10x\cdot2-15x+9 &= 0&& \text{simplify left side} \\[1 em](2x^2+3x-1)^2-20x-15x+9 &= 0&& \\[1 em]4x^4+12x^3+5x^2-6x+1-20x-15x+9 &= 0&& \\[1 em]4x^4+12x^3+5x^2-41x+10 &= 0&& \\[1 em] \end{aligned} $$
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