Make sure you write all the terms on the left-hand side of the equation and simplify as much as possible before using the Quadratic Formula.
Solution: x= 13, x=- 6 Does the solution match? Yes.
Practice makes perfect
We will use the Quadratic Formula to solve the given quadratic equation.
ax^2+ bx+ c=0 ⇕ x=- b± sqrt(b^2-4 a c)/2 a
Let's start by rearranging the equation so all of the terms are on the left-hand side of the equation.
0=3x^2+17x-6
⇕
3x^2+17x-6=0
Now we can identify the values of a, b, and c.
3x^2+17x-6=0 ⇕ 3x^2+ 17x+( - 6)=0
We see that a= 3, b= 17, and c= - 6. Let's substitute these values into the Quadratic Formula.
The solutions for this equation are x= - 17± 196. Let's separate them into the positive and negative cases.
x=- 17± 19/6
x_1=- 17+19/6
x_2=- 17-19/6
x_1=2/6
x_2=- 36/6
x_1=1/3
x_2=- 6
Using the Quadratic Formula, we found that the solutions are x_1= 13 and x_2=- 6. Notice that those are the same solutions as obtained in Part B of the previous exercise, where we solved the equation by factoring and then using Zero Product Property. Both methods are equally good, so they give the same solutions.
