3x=10/13x

Solution for 3x=10/13x equation:

3x=10/13x

We move all terms to the left:

3x-(10/13x)=0


Domain of the equation: 13x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(+10/13x)=0

We get rid of parentheses

3x-10/13x=0

We multiply all the terms by the denominator


3x*13x-10=0

Wy multiply elements

39x^2-10=0

a = 39; b = 0; c = -10;
Δ = b2-4ac
Δ = 02-4·39·(-10)
Δ = 1560
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:

$\sqrt{\Delta}=\sqrt{1560}=\sqrt{4*390}=\sqrt{4}*\sqrt{390}=2\sqrt{390}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{390}}{2*39}=\frac{0-2\sqrt{390}}{78}
=-\frac{2\sqrt{390}}{78}
=-\frac{\sqrt{390}}{39}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{390}}{2*39}=\frac{0+2\sqrt{390}}{78}
=\frac{2\sqrt{390}}{78}
=\frac{\sqrt{390}}{39}
$