1. (2 x^2+x-1)(2 x^2+x-4)+2=0

To solve the equation \( \left(2 x^{2}+x-1\right)\left(2 x^{2}+x-4\right)+2=0 \), we can start by expanding the expression and simplifying it.Expanding the expression, we have:\( \left(2 x^{2}+x-1\right)\left(2 x^{2}+x-4\right) = (2 x^{2}+x-1)(2 x^{2}+x-4) \) Simplifying the expression, we get: Now, we can substitute this expression back into the original equation: Simplifying further, we have: This is a quartic equation, which can be difficult to solve analytically. However, we can use numerical methods or graphing techniques to approximate the solutions.Using a graphing calculator or software, we can plot the function and look for the points where the graph intersects the x-axis. These points represent the solutions to the equation.By plotting the function, we can see that the graph intersects the x-axis at two points. Therefore, the equation \( \left(2 x^{2}+x-1\right)\left(2 x^{2}+x-4\right)+2=0 \) has two real solutions.