Final answer:
To solve the equation 10u(u + 1) + 3 = 0 using the quadratic formula, the quadratic has no real solutions.
Step-by-step explanation:
To solve the equation 10u(u + 1) + 3 = 0 using the quadratic formula, we first need to rearrange the equation to get 0 on one side:
10u(u + 1) + 3 = 0
10u^2 + 10u + 3 = 0
Now we can identify that a = 10, b = 10, and c = 3. Substituting these values into the quadratic formula:
u = (-b ± √(b^2 - 4ac)) / (2a)
we can solve for u:
u = (-10 ± √(10^2 - 4*10*3)) / (2*10)
Simplifying further, we have:
u = (-10 ± √(100 - 120)) / 20
u = (-10 ± √(-20)) / 20
Since the quadratic has no real solutions (the discriminant is negative), the equation has no real roots.