5/6x=55x

Solution for 5/6x=55x equation:

5/6x=55x

We move all terms to the left:

5/6x-(55x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

-55x+5/6x=0

We multiply all the terms by the denominator


-55x*6x+5=0

Wy multiply elements

-330x^2+5=0

a = -330; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-330)·5
Δ = 6600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6600}=\sqrt{100*66}=\sqrt{100}*\sqrt{66}=10\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{66}}{2*-330}=\frac{0-10\sqrt{66}}{-660}
=-\frac{10\sqrt{66}}{-660}
=-\frac{\sqrt{66}}{-66}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{66}}{2*-330}=\frac{0+10\sqrt{66}}{-660}
=\frac{10\sqrt{66}}{-660}
=\frac{\sqrt{66}}{-66}
$