6-1/2x=1+2x

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

6-1/2x=1+2x

We move all terms to the left:

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-4x^2-2x+12x-1=0

We add all the numbers together, and all the variables

-4x^2+10x-1=0

a = -4; b = 10; c = -1;
Δ = b2-4ac
Δ = 102-4·(-4)·(-1)
Δ = 84
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{21}}{2*-4}=\frac{-10-2\sqrt{21}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{21}}{2*-4}=\frac{-10+2\sqrt{21}}{-8}
$