SOLUTION: Can you please explain this to me? Solve using the quadratic formula 3x^2 - 2x = 15x

SOLUTION: Can you please explain this to me? Solve using the quadratic formula 3x^2 - 2x = 15x - 10 thank you julie

Question 118222: Can you please explain this to me?
Solve using the quadratic formula
3x^2 - 2x = 15x - 10
thank you
julie
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given equation

Subtract 15x from both sides. Add 10 to both sides.

Combine like terms

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=3, b=-17, and c=10

Negate -17 to get 17

Square -17 to get 289 (note: remember when you square -17, you must square the negative as well. This is because .)

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 3 to get 6

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator
Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator
Divide

So another answer is

So our solutions are:
or

Notice when we graph , we get:

and we can see that the roots are and . This verifies our answer

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