2x+(4/6x)-1.365x=16.78x

Solution for 2x+(4/6x)-1.365x=16.78x equation:

2x+(4/6x)-1.365x=16.78x

We move all terms to the left:

2x+(4/6x)-1.365x-(16.78x)=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-(+16.78x)=0

We add all the numbers together, and all the variables

0.635x+(+4/6x)-(+16.78x)=0

We get rid of parentheses

0.635x+4/6x-16.78x=0

We multiply all the terms by the denominator


(0.635x)*6x-(16.78x)*6x+4=0

We add all the numbers together, and all the variables

(+0.635x)*6x-(+16.78x)*6x+4=0

We multiply parentheses

0x^2-96x^2+4=0

We add all the numbers together, and all the variables

-95x^2+4=0

a = -95; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-95)·4
Δ = 1520
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:

$\sqrt{\Delta}=\sqrt{1520}=\sqrt{16*95}=\sqrt{16}*\sqrt{95}=4\sqrt{95}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{95}}{2*-95}=\frac{0-4\sqrt{95}}{-190}
=-\frac{4\sqrt{95}}{-190}
=-\frac{2\sqrt{95}}{-95}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{95}}{2*-95}=\frac{0+4\sqrt{95}}{-190}
=\frac{4\sqrt{95}}{-190}
=\frac{2\sqrt{95}}{-95}
$