The quadratic formula, for the equation ax² + bx + c = 0, where a ≠ 0, is:
x = (-b plus or minus √(b² - 4ac)) ÷ 2a. From this formula...
...the discriminant of ax² + bx + c = 0 is given by Δ = b² - 4ac.
If Δ > 0, then there are two real roots. If Δ < 0, there are no real solutions.
If Δ = 0, there is exactly 1 real root.
Using this, we can substitute the coefficients for j into the discriminant formula. Δ = 3² - 4(-4)(-28), which equals 9 - (448), which is clearly less than 0.
So there are NO REAL ROOTS to -4j² + 3j - 28 = 0
Hope this helps!
