6x-4=1/210x

Solution for 6x-4=1/210x equation:

6x-4=1/210x

We move all terms to the left:

6x-4-(1/210x)=0


Domain of the equation: 210x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6x-(+1/210x)-4=0

We get rid of parentheses

6x-1/210x-4=0

We multiply all the terms by the denominator


6x*210x-4*210x-1=0

Wy multiply elements

1260x^2-840x-1=0

a = 1260; b = -840; c = -1;
Δ = b2-4ac
Δ = -8402-4·1260·(-1)
Δ = 710640
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:

$\sqrt{\Delta}=\sqrt{710640}=\sqrt{144*4935}=\sqrt{144}*\sqrt{4935}=12\sqrt{4935}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-840)-12\sqrt{4935}}{2*1260}=\frac{840-12\sqrt{4935}}{2520}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-840)+12\sqrt{4935}}{2*1260}=\frac{840+12\sqrt{4935}}{2520}
$