2x+1/3x-4=2.5

Solution for 2x+1/3x-4=2.5 equation:

2x+1/3x-4=2.5

We move all terms to the left:

2x+1/3x-4-(2.5)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2x+1/3x-6.5=0

We multiply all the terms by the denominator


2x*3x-(6.5)*3x+1=0

We multiply parentheses

2x*3x-19.5x+1=0

Wy multiply elements

6x^2-19.5x+1=0

a = 6; b = -19.5; c = +1;
Δ = b2-4ac
Δ = -19.52-4·6·1
Δ = 356.25
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{-(-19.5)-\sqrt{356.25}}{2*6}=\frac{19.5-\sqrt{356.25}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19.5)+\sqrt{356.25}}{2*6}=\frac{19.5+\sqrt{356.25}}{12}
$