3x-1/2x=2.5

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

3x-1/2x=2.5

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3x-1/2x-2.5=0

We multiply all the terms by the denominator


3x*2x-(2.5)*2x-1=0

We multiply parentheses

3x*2x-5x-1=0

Wy multiply elements

6x^2-5x-1=0

a = 6; b = -5; c = -1;
Δ = b2-4ac
Δ = -52-4·6·(-1)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-7}{2*6}=\frac{-2}{12}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+7}{2*6}=\frac{12}{12}
=1
$