SOLUTION: Solve using the quadratic formula please: Please help me with step by step instructions to help me understand. Thank you in advance! C

Question 119765: Solve using the quadratic formula please:

Please help me with step by step instructions to help me understand.
Thank you in advance!
C
Found 3 solutions by Caallen2, jim_thompson5910, madhan_math:
Answer by Caallen2(9)   (Show Source): You can put this solution on YOUR website!
To begin you need to make one side equal to zero to get the total equation so you can solve for x.
3x^2-2x = 15x-10
subtract 15x and -10 from both sides
3x^2 - 2x - 15x - (-10)= 15x - 10 - 15x - (-10)
Simplify
3x^2 - 17x +10 = 0
Now you will break down this equation into two simpler equations. To do this you must determine which factors are needed. For example we know that 3's factors are only 3 and 1, however for 10 the factors are either 10 and 1 or 5 and 2. To determine which of these two to use you must look to the middle number, which is 17x. The factors that would make - 17x would be - 5 and -2 where 5 is going to be the factor that is multipled by 3x and 2 is the factor being multiplied by 1x.
(3x - 2)(x - 5) = 0
3x - 2 = 0 and x - 5 = 0
start with 3x - 2 = 0
add 2 to both sides
3x - 2 + 2 = 0 + 2
3x = 2
divide both sides by 3
3x/3 = 2/3
x = 2/3
now for the second part
x - 5 = 0
add 5 to both sides
x - 5 + 5 = 0 + 5
x = 5
So your solution will be x = 2/3, 5
To check your solution plug one of the answers for x into your orginal equation and solve.

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

Answer by madhan_math(34)   (Show Source): You can put this solution on YOUR website!
3x^2-2x=15x-10.
Solution:
you rearrange the equation into the form 3x(x)-2(x)and then you take (x)=5.
This implies that 3x^2-2x=15x-10
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