In this quadratic equation, 5t²+5t+6=0, to find the discriminant we use the formula D=b²-4ac, where 'a', 'b' and 'c' are the coefficients of the equation. Here, 'a' is the coefficient of t², 'b' is the coefficient of 't', and 'c' is the constant term.
Step 1: Identify the coefficients in the given equation.
'a' = 5, 'b' = 5, and 'c' = 6.
Step 2: Substitute the values of 'a', 'b' and 'c' into the discriminant formula (D=b²-4ac).
D = (5)² - 4*(5)*(6)
Step 3: Simplify the operation inside the parentheses before moving on to the multiplication and subtraction.
= 25 - 4*5*6
Step 4: Continue with the multiplication operation.
= 25 - 120
Step 5: Finish by carrying out the subtraction operation.
The discriminant D = -95
If the discriminant of a quadratic equation is negative (as it is here, -95), it means that the equation has no real roots. Instead, the solutions would be complex or imaginary.