SOLUTION: 6r^2=13r-5

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: 6r^2=13r-5      Log On


   

Question 1049874: 6r^2=13r-5
Found 2 solutions by srinivas.g, ewatrrr:
Answer by srinivas.g(540) About Me  (Show Source):
You can put this solution on YOUR website!
Given that
+6+%2Ar%5E2+=+13%2Ar+-5
move 13r -5 to the left
+6+%2Ar%5E2+-13%2Ar+%2B5+=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ar%5E2%2Bbr%2Bc=0 (in our case 6r%5E2%2B-13r%2B5+=+0) has the following solutons:

r%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-13%29%5E2-4%2A6%2A5=49.

Discriminant d=49 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--13%2B-sqrt%28+49+%29%29%2F2%5Ca.

r%5B1%5D+=+%28-%28-13%29%2Bsqrt%28+49+%29%29%2F2%5C6+=+1.66666666666667
r%5B2%5D+=+%28-%28-13%29-sqrt%28+49+%29%29%2F2%5C6+=+0.5

Quadratic expression 6r%5E2%2B-13r%2B5 can be factored:
6r%5E2%2B-13r%2B5+=+6%28r-1.66666666666667%29%2A%28r-0.5%29
Again, the answer is: 1.66666666666667, 0.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B-13%2Ax%2B5+%29

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
6r^2-13r+5 = 0
r+=+%2813+%2B-+sqrt%28+169-120+%29%29%2F%2812%29+
r+=+%2813+%2B-+7%29%2F%2812%29+
r = 20/12 = 5/3
r = 6/12 = 1/2
0r
factoring:
6r^2-13r+5 = 0
(3r - 5)(2r - 1) = 0
r = 5/3
r = 1/2