11/6x=x=49

Solution for 11/6x=x=49 equation:

11/6x=x=49

We move all terms to the left:

11/6x-(x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+11/6x=0

We multiply all the terms by the denominator


-1x*6x+11=0

Wy multiply elements

-6x^2+11=0

a = -6; b = 0; c = +11;
Δ = b2-4ac
Δ = 02-4·(-6)·11
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{66}}{2*-6}=\frac{0-2\sqrt{66}}{-12}
=-\frac{2\sqrt{66}}{-12}
=-\frac{\sqrt{66}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{66}}{2*-6}=\frac{0+2\sqrt{66}}{-12}
=\frac{2\sqrt{66}}{-12}
=\frac{\sqrt{66}}{-6}
$