/x+1.5-x+0.5=3x-2

Solution for /x+1.5-x+0.5=3x-2 equation:

/x+1.5-x+0.5=3x-2

We move all terms to the left:

/x+1.5-x+0.5-(3x-2)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

4x-1x*x-3x*x=0

Wy multiply elements

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

We add all the numbers together, and all the variables

-4x^2+4x=0

a = -4; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-4)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-4}=\frac{-8}{-8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-4}=\frac{0}{-8}
=0
$