SOLUTION: Please help me solve this equation: {{{log6 x + log6 (2x+1)=2 }}} Thank you very much.

Question 339442: Please help me solve this equation:

Thank you very much.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!

x={4, -4.5}
The negative solution is extraneous, throw it out leaving:
x = 4
.
Details of quadratic to follow:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=289 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 4, -4.5. Here's your graph:

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