Final answer:
The discriminant of the quadratic equation 7x²+6x+3=0 is found by substituting the coefficients into the formula b²-4ac, which yields a value of -48. Therefore, the equation has no real solutions as the roots are complex numbers.
Step-by-step explanation:
The discriminant of a quadratic equation ax²+bx+c=0 is given by the formula b²-4ac. For the quadratic equation 7x²+6x+3=0, the coefficients are a=7, b=6, and c=3. To find the discriminant of this equation, substitute these values into the formula:
Discriminant = b²-4ac
Discriminant = (6)² - 4(7)(3)
Discriminant = 36 - 84
Discriminant = -48
So, the discriminant of the equation 7x²+6x+3=0 is -48. The negative value of the discriminant indicates that this quadratic equation has no real solutions because the roots are complex numbers.