5/6x=20;x

Solution for 5/6x=20;x equation:

5/6x=20x

We move all terms to the left:

5/6x-(20x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

-20x+5/6x=0

We multiply all the terms by the denominator


-20x*6x+5=0

Wy multiply elements

-120x^2+5=0

a = -120; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-120)·5
Δ = 2400
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:

$\sqrt{\Delta}=\sqrt{2400}=\sqrt{400*6}=\sqrt{400}*\sqrt{6}=20\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{6}}{2*-120}=\frac{0-20\sqrt{6}}{-240}
=-\frac{20\sqrt{6}}{-240}
=-\frac{\sqrt{6}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{6}}{2*-120}=\frac{0+20\sqrt{6}}{-240}
=\frac{20\sqrt{6}}{-240}
=\frac{\sqrt{6}}{-12}
$