2.5x=13+1/3x

Solution for 2.5x=13+1/3x equation:

2.5x=13+1/3x

We move all terms to the left:

2.5x-(13+1/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2.5x-(1/3x+13)=0

We get rid of parentheses

2.5x-1/3x-13=0

We multiply all the terms by the denominator


(2.5x)*3x-13*3x-1=0

We add all the numbers together, and all the variables

(+2.5x)*3x-13*3x-1=0

We multiply parentheses

6x^2-13*3x-1=0

Wy multiply elements

6x^2-39x-1=0

a = 6; b = -39; c = -1;
Δ = b2-4ac
Δ = -392-4·6·(-1)
Δ = 1545
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-\sqrt{1545}}{2*6}=\frac{39-\sqrt{1545}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{1545}}{2*6}=\frac{39+\sqrt{1545}}{12}
$