5/6x-x=6x

Solution for 5/6x-x=6x equation:

5/6x-x=6x

We move all terms to the left:

5/6x-x-(6x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

-7x+5/6x=0

We multiply all the terms by the denominator


-7x*6x+5=0

Wy multiply elements

-42x^2+5=0

a = -42; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-42)·5
Δ = 840
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:

$\sqrt{\Delta}=\sqrt{840}=\sqrt{4*210}=\sqrt{4}*\sqrt{210}=2\sqrt{210}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{210}}{2*-42}=\frac{0-2\sqrt{210}}{-84}
=-\frac{2\sqrt{210}}{-84}
=-\frac{\sqrt{210}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{210}}{2*-42}=\frac{0+2\sqrt{210}}{-84}
=\frac{2\sqrt{210}}{-84}
=\frac{\sqrt{210}}{-42}
$