2x+(4/6x)-1.365x=8x

Solution for 2x+(4/6x)-1.365x=8x equation:

2x+(4/6x)-1.365x=8x

We move all terms to the left:

2x+(4/6x)-1.365x-(8x)=0


Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x+(+4/6x)-1.365x-8x=0

We add all the numbers together, and all the variables

-7.365x+(+4/6x)=0

We get rid of parentheses

-7.365x+4/6x=0

We multiply all the terms by the denominator


-(7.365x)*6x+4=0

We add all the numbers together, and all the variables

-(+7.365x)*6x+4=0

We multiply parentheses

-42x^2+4=0

a = -42; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-42)·4
Δ = 672
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:

$\sqrt{\Delta}=\sqrt{672}=\sqrt{16*42}=\sqrt{16}*\sqrt{42}=4\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{42}}{2*-42}=\frac{0-4\sqrt{42}}{-84}
=-\frac{4\sqrt{42}}{-84}
=-\frac{\sqrt{42}}{-21}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{42}}{2*-42}=\frac{0+4\sqrt{42}}{-84}
=\frac{4\sqrt{42}}{-84}
=\frac{\sqrt{42}}{-21}
$