2x²-3x+4>0;

To solve the inequality 2x² - 3x + 4 > 0, we can use the quadratic formula or graphing techniques. Let's solve it using the quadratic formula.

The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions can be found using:

x = (-b ± √(b² - 4ac)) / (2a)

In our case, the equation is 2x² - 3x + 4 > 0. We need to find the values of x for which this inequality is true.

First, let's find the roots of the equation 2x² - 3x + 4 = 0:

x = (-(-3) ± √((-3)² - 4(2)(4))) / (2(2)) x = (3 ± √(9 - 32)) / 4 x = (3 ± √(-23)) / 4

Since we have a negative value inside the square root, there are no real solutions for this equation. So, the graph of the equation 2x² - 3x + 4 will not intersect the x-axis.

Therefore, it will either be always positive or always negative. To determine which one, we can examine the coefficient of x², which is 2. Since this is positive, the parabola will open upwards, indicating that its value will be positive for all x.

Hence, the solution to the inequality 2x² - 3x + 4 > 0 is: x ∈ (-∞, +∞)