3x=13/5x=2

Solution for 3x=13/5x=2 equation:

3x=13/5x=2

We move all terms to the left:

3x-(13/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(+13/5x)=0

We get rid of parentheses

3x-13/5x=0

We multiply all the terms by the denominator


3x*5x-13=0

Wy multiply elements

15x^2-13=0

a = 15; b = 0; c = -13;
Δ = b2-4ac
Δ = 02-4·15·(-13)
Δ = 780
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:

$\sqrt{\Delta}=\sqrt{780}=\sqrt{4*195}=\sqrt{4}*\sqrt{195}=2\sqrt{195}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{195}}{2*15}=\frac{0-2\sqrt{195}}{30}
=-\frac{2\sqrt{195}}{30}
=-\frac{\sqrt{195}}{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{195}}{2*15}=\frac{0+2\sqrt{195}}{30}
=\frac{2\sqrt{195}}{30}
=\frac{\sqrt{195}}{15}
$