SOLUTION: Solve each equation by using the quadratic formula. 3a^2-4a=-5

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Question 526676: Solve each equation by using the quadratic formula.
3a^2-4a=-5
Found 2 solutions by oberobic, stanbon:
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aa%5E2%2Bba%2Bc=0 (in our case 3a%5E2%2B-4a%2B5+=+0) has the following solutons:

a%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=%28-4%29%5E2-4%2A3%2A5=-44.

The discriminant -44 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -44 is + or - sqrt%28+44%29+=+6.6332495807108.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-4%2Ax%2B5+%29

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Solve each equation by using the quadratic formula.
3a^2-4a=-5
----
3a^2-4a+5 = 0
---
a = [4 +- sqrt(16-4*3*5)]/6
----
a = [4 +- sqrt(-44)]/6
-----
a = [4+- 2*sqrt(11)]/6
---
a = (2/3)+-(1/3)sqrt(11)
===========================
Cheers,
Stan H.
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