3x+2=1/2x+2.5

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

3x+2=1/2x+2.5

We move all terms to the left:

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


Domain of the equation: 2x+2.5)!=0

x∈R


We get rid of parentheses

3x-1/2x-2.5+2=0

We multiply all the terms by the denominator


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

We multiply parentheses

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

Wy multiply elements

6x^2-5x+4x-1=0

We add all the numbers together, and all the variables

6x^2-1x-1=0

a = 6; b = -1; c = -1;
Δ = b2-4ac
Δ = -12-4·6·(-1)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5}{2*6}=\frac{-4}{12}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5}{2*6}=\frac{6}{12}
=1/2
$