1/2x+6+3/2x=10+2x-4

Solution for 1/2x+6+3/2x=10+2x-4 equation:

1/2x+6+3/2x=10+2x-4

We move all terms to the left:

1/2x+6+3/2x-(10+2x-4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x+3/2x-(2x+6)+6=0

We get rid of parentheses

1/2x+3/2x-2x-6+6=0

We multiply all the terms by the denominator


-2x*2x-6*2x+6*2x+1+3=0

We add all the numbers together, and all the variables

-2x*2x-6*2x+6*2x+4=0

Wy multiply elements

-4x^2-12x+12x+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
$