0.5x+2=1/6x-1

Solution for 0.5x+2=1/6x-1 equation:

0.5x+2=1/6x-1

We move all terms to the left:

0.5x+2-(1/6x-1)=0


Domain of the equation: 6x-1)!=0

x∈R


We get rid of parentheses

0.5x-1/6x+1+2=0

We multiply all the terms by the denominator


(0.5x)*6x+1*6x+2*6x-1=0

We add all the numbers together, and all the variables

(+0.5x)*6x+1*6x+2*6x-1=0

We multiply parentheses

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

Wy multiply elements

0x^2+6x+12x-1=0

We add all the numbers together, and all the variables

x^2+18x-1=0

a = 1; b = 18; c = -1;
Δ = b2-4ac
Δ = 182-4·1·(-1)
Δ = 328
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:

$\sqrt{\Delta}=\sqrt{328}=\sqrt{4*82}=\sqrt{4}*\sqrt{82}=2\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{82}}{2*1}=\frac{-18-2\sqrt{82}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{82}}{2*1}=\frac{-18+2\sqrt{82}}{2}
$