Question 934389
You have no quadratic equation.


{{{log (5,x)+log (5, (4x-1))=1}}}, what your actual text really shows inside the rendering tags;


{{{log(5,(x(4x-1)))=1}}}


The LOGARITHM is the EXPONENT.
The BASE used is 5.
Change into exponential form.


{{{5^1=x(4x-1)}}}, which you should have no further trouble to solve.




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The rendering does not always clarify certain things.  Your original text was log (5,x)+log (5, 4x-1)=1
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You clearly want {{{4x-1}}} to be the expression in a logarithm function.  I then included left and right parentheses around the expression, which ensured that the -1 part would appear in the intended position; otherwise, your original text makes the -1 appear to be outside the logarithm function, which would NOT be what you intended.   I had planned to ADD 1 to left and right sides of the equation and this would have been in disagreement with your equation.