1/6x-0.5=3-0.5x

Solution for 1/6x-0.5=3-0.5x equation:

1/6x-0.5=3-0.5x

We move all terms to the left:

1/6x-0.5-(3-0.5x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

1/6x-(-0.5x+3)-0.5=0

We get rid of parentheses

1/6x+0.5x-3-0.5=0

We multiply all the terms by the denominator


(0.5x)*6x-3*6x-(0.5)*6x+1=0

We add all the numbers together, and all the variables

(+0.5x)*6x-3*6x-(0.5)*6x+1=0

We multiply parentheses

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

Wy multiply elements

0x^2-18x-3x+1=0

We add all the numbers together, and all the variables

x^2-21x+1=0

a = 1; b = -21; c = +1;
Δ = b2-4ac
Δ = -212-4·1·1
Δ = 437
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{437}}{2*1}=\frac{21-\sqrt{437}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{437}}{2*1}=\frac{21+\sqrt{437}}{2}
$