1/2*x+6=-1/2*x+10

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

1/2*x+6=-1/2*x+10

We move all terms to the left:

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


Domain of the equation: 2*x!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 2*x+10)!=0

x∈R


We get rid of parentheses

1/2*x+1/2*x-10+6=0

We multiply all the terms by the denominator


-10*2*x+6*2*x+1+1=0

We add all the numbers together, and all the variables

-10*2*x+6*2*x+2=0

Wy multiply elements

-20x*x+12x*x+2=0

Wy multiply elements

-20x^2+12x^2+2=0

We add all the numbers together, and all the variables

-8x^2+2=0

a = -8; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-8)·2
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*-8}=\frac{-8}{-16}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8}{2*-8}=\frac{8}{-16}
=-1/2
$