x=56x-13/3x

Solution for x=56x-13/3x equation:

x=56x-13/3x

We move all terms to the left:

x-(56x-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-(+56x-13/3x)=0

We get rid of parentheses

x-56x+13/3x=0

We multiply all the terms by the denominator


x*3x-56x*3x+13=0

Wy multiply elements

3x^2-168x^2+13=0

We add all the numbers together, and all the variables

-165x^2+13=0

a = -165; b = 0; c = +13;
Δ = b2-4ac
Δ = 02-4·(-165)·13
Δ = 8580
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:

$\sqrt{\Delta}=\sqrt{8580}=\sqrt{4*2145}=\sqrt{4}*\sqrt{2145}=2\sqrt{2145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{2145}}{2*-165}=\frac{0-2\sqrt{2145}}{-330}
=-\frac{2\sqrt{2145}}{-330}
=-\frac{\sqrt{2145}}{-165}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{2145}}{2*-165}=\frac{0+2\sqrt{2145}}{-330}
=\frac{2\sqrt{2145}}{-330}
=\frac{\sqrt{2145}}{-165}
$