Answer:
No real solutions
Step-by-step explanation:
Discriminant
[tex]b^2-4ac\quad\textsf{when}\:ax^2+bx+c=0[/tex]
[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real solutions}[/tex]
[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real solution}[/tex]
[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real solutions}[/tex]
Given equation: [tex]6x^2+6x+3=0[/tex]
[tex]\implies a=6, \quad b=6, \quad c=3[/tex]
Inputting these values into the discriminant:
[tex]\implies (6)^2-4(6)(3)=-36 < 0\implies \textsf{no real solutions}[/tex]
