SOLUTION: Solve equation with quadratic formula 3n^2-15=-4n

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Solve equation with quadratic formula 3n^2-15=-4n      Log On


   

Question 201620: Solve equation with quadratic formula
3n^2-15=-4n
Found 2 solutions by Earlsdon, jsmallt9:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for n:
3n%5E2-15+=+-4n Add 4n to both sides.
3n%5E2%2B4n-15+=+0 Factor.
%283n-5%29%28n%2B3%29+=+0 Apply the zero product rule.
3n-5+=+0 or n%2B3+=+0 so...
3n+=+5 and highlight%28n+=+5%2F3%29 or
highlight%28n+=+-3%29

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
To use the quadratic formula we must first get the equation into the form:
ax%5E2+%2B+bx+%2B+c+=+0
This means:
  1. Get one side equal to zero
  2. Use the Commutative property of addition to rearrange the non-zero side in order from highest exponent to lowest.

Using these steps on your equation: 3n%5E2+-+15+=+-4n
1. Make one side zero. By adding 4n to both sides the right side will become zero:
3n%5E2+-+15+%2B+4n+=+0
2. Change subtractions to additions
3n%5E2+%2B+%28-15%29+%2B+4n+=+0
3. Rearrange
3n%5E2+%2B+4n+%2B+%28-15%29+=+0

Now we have the equation in the proper form for the quadratic formula:
x+=+%28-b+%2B-+sqrt%28b%5E2+-+4ac%29%29%2F2a
Looking at your rearranged equation we should be able to tell that
a = 3
b = 4
c = -15
Substituting these into the appropriate places in the formula we get:
x+=+%28+-%284%29+%2B-+sqrt%28%284%29%5E2+-+4%283%29%28-15%29%29%29%2F2%283%29
Squaring the 4
x+=+%28+-4+%2B-+sqrt%2816+-+4%283%29%28-15%29%29%29%2F2%283%29
Multiplying
x+=+%28+-4+%2B-+sqrt%2816+-+%28-180%29%29%29%2F6
Simplifying inside the square root
x+=+%28+-4+%2B-+sqrt%28196%29%29%2F6
sqrt%28196%29+=+14 Substituting we get
x+=+%28-4+%2B-+14%29%2F6
Splitting the +- we get
x+=+%28-4+%2B+14%29%2F6 or x+=+%28-4+-+14%29%2F6
Simplifying each:
x+=+10%2F6+=+1%264%2F6+=+1%262%2F3 or x+=+-18%2F6+=+-3
The solutions:
x+=+1%262%2F3 or x+=+-3