Final answer:
To solve the quadratic equation a(9a+20)+6=0, expand it to 9a²+20a+6=0 and apply the quadratic formula with a=9, b=20, and c=6. The discriminant will determine the number of real solutions.
Step-by-step explanation:
Solving Quadratic Equation Using the Quadratic Formula
To solve the quadratic equation a(9a+20)+6=0, we need to expand it and rearrange it to the general form of a quadratic equation, which is ax²+bx+c = 0. After expanding, the equation takes the form 9a² + 20a + 6 = 0.
Next, we apply the quadratic formula which is given as:
x = √[(-b ± √(b²-4ac)) / (2a)]
Here, the coefficients are a = 9, b = 20, and c = 6. Substituting these into the quadratic formula, we can find the solution(s) to the quadratic equation. Remember, the discriminant (b²-4ac) will indicate how many real solutions exist. If it's positive, there are two real solutions; if it's zero, there is one real solution; and if it's negative, there are no real solutions.