Can someone explain it to me, i don't need the answer, i just need an detailed explanation of how they got the answer using the method that they provided

Step-by-step explanation:

Good idea to review quadratic functions and the quadratic formula.

Quadratics have three coefficients:  ax² + bx + c, and the "discriminant" is defined as b²-4ac.  Please review these rules:

1) if the discriminant is +, the quadratic equation has two real, unequal roots.

2) if the disc. is 0, the equation has two real, equal root.

3) If the disc. is - , the equation has two complex roots.

Here a = 1, b  = -3 and c = 4.  Therefore the discriminant is (-3)²-4(1)(4), or

-7.  Rule 3) applies:  the equation has two complex roots, but no real ones.  Thus we know that the graph does not cross the x-axis.

Graphing the given quadratic, x² - 3x + 4, using a dashed "line," is helpful.  As you can see in the illustration of this graph, the graph neither touches nor crosses the x-axis.  Thus, y = x² - 3x + 4 is greater than 0 for all x.  The  All real numbers.