Answer:
3v²+6v+6=0
3v²+6v+6 is an equation of the form:
ax²+bx+c=0
where a,b,c are real coefficients
a=3; b=6; c=6
We set Δ=b²−4ac
. Δ is called the trinomial discriminant ax²+bx+c. The number of solutions of the equation depends on the sign of the discriminant.
Δ<0: no solution
Δ=0:1solution:-b/2a
Δ>0 2solutions
we calculate Δ: 6²-4(3*6)=36-72=-36
Δ<0; no real solution
The discriminant Δ is strictly negative, the equation 3x²+6x+6=0
admits no real solution but admits two COMPLEX solutions:
solution 1: (-b-iV-Δ)/2a =(-6-i6)/6 = -1-i
solution 2: (-b+iV-Δ)/2a= (-6+i6)/6 =- 1+i