SOLUTION: Solve by using the quadratic formula: 3x^2+4x-15=0

Question 116773: Solve by using the quadratic formula: 3x^2+4x-15=0
Found 2 solutions by jim_thompson5910, bucky:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
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=4, and c=-15

Square 4 to get 16

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 bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.

.
This is in the standard quadratic form of:
.

.
By comparing the standard form to the given problem, you can see that a = 3, b = 4, and c = -15
.
For the standard form, the values of x that satisfy the equation are given by:
.

.
So all you have to do to solve the given equation is to substitute 3 for a, 4 for b, and -15
for c into the equation for x. When you do, that equation becomes:
.

.
Multiply out the denominator 2*3 = 6 to make the equation become:
.

.
Work inside the radical. and and substituting
these values results in:
.

.
Combine the terms in the radical:
.

.
But the square root of 196 is 14. Substituting this results in:
.

.
Note that -(4) = -4 which simplifies the equation to:
.

.
So there are two possible values of x as follows:
.

.
and
.

.
Those are the two answers. Hope this helps to familiarize you with the quadratic equation and
how it can be used to solve quadratic equations.
.
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