x=46x-13/3x

Solution for x=46x-13/3x equation:

x=46x-13/3x

We move all terms to the left:

x-(46x-13/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+46x-13/3x)=0

We get rid of parentheses

x-46x+13/3x=0

We multiply all the terms by the denominator


x*3x-46x*3x+13=0

Wy multiply elements

3x^2-138x^2+13=0

We add all the numbers together, and all the variables

-135x^2+13=0

a = -135; b = 0; c = +13;
Δ = b2-4ac
Δ = 02-4·(-135)·13
Δ = 7020
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:

$\sqrt{\Delta}=\sqrt{7020}=\sqrt{36*195}=\sqrt{36}*\sqrt{195}=6\sqrt{195}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{195}}{2*-135}=\frac{0-6\sqrt{195}}{-270}
=-\frac{6\sqrt{195}}{-270}
=-\frac{\sqrt{195}}{-45}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{195}}{2*-135}=\frac{0+6\sqrt{195}}{-270}
=\frac{6\sqrt{195}}{-270}
=\frac{\sqrt{195}}{-45}
$