1/2x+3x-2=5x-3/2x+5-7

Solution for 1/2x+3x-2=5x-3/2x+5-7 equation:

1/2x+3x-2=5x-3/2x+5-7

We move all terms to the left:

1/2x+3x-2-(5x-3/2x+5-7)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 2x+5-7)!=0

We move all terms containing x to the left, all other terms to the right

2x-7)!=-5

x∈R


We add all the numbers together, and all the variables

1/2x+3x-(5x-3/2x-2)-2=0

We add all the numbers together, and all the variables

3x+1/2x-(5x-3/2x-2)-2=0

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

3x*2x-5x*2x+2*2x-2*2x+4=0

Wy multiply elements

6x^2-10x^2+4x-4x+4=0

We add all the numbers together, and all the variables

-4x^2+4=0

a = -4; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-4)·4
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8}{2*-4}=\frac{-8}{-8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8}{2*-4}=\frac{8}{-8}
=-1
$