Question

find the discriminant.
$6u^2 + 6u = -6$
how many real solutions does the equation have?
no real solutions
one real solution
two real solutions

Explanation:

Step1: Rewrite in standard form

$6u^2 + 6u + 6 = 0$

Step2: Identify a, b, c

$a=6,\ b=6,\ c=6$

Step3: Calculate discriminant

$\Delta = b^2 - 4ac = 6^2 - 4(6)(6)$
$\Delta = 36 - 144 = -108$

Step4: Analyze discriminant sign

Since $\Delta < 0$, there are no real solutions.

Answer:

Discriminant: $\boldsymbol{-108}$
Number of real solutions: no real solutions