3x-1,5=-1/2x+2

Solution for 3x-1,5=-1/2x+2 equation:

3x-1.5=-1/2x+2

We move all terms to the left:

3x-1.5-(-1/2x+2)=0


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

x∈R


We get rid of parentheses

3x+1/2x-2-1.5=0

We multiply all the terms by the denominator


3x*2x-2*2x-(1.5)*2x+1=0

We multiply parentheses

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

Wy multiply elements

6x^2-4x-3x+1=0

We add all the numbers together, and all the variables

6x^2-7x+1=0

a = 6; b = -7; c = +1;
Δ = b2-4ac
Δ = -72-4·6·1
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{-(-7)-5}{2*6}=\frac{2}{12}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+5}{2*6}=\frac{12}{12}
=1
$