.5x+2=1/6x-1

Solution for .5x+2=1/6x-1 equation:

.5x+2=1/6x-1

We move all terms to the left:

.5x+2-(1/6x-1)=0


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

x∈R


We get rid of parentheses

.5x-1/6x+1+2=0

We multiply all the terms by the denominator


(.5x)*6x+1*6x+2*6x-1=0

We add all the numbers together, and all the variables

(+.5x)*6x+1*6x+2*6x-1=0

We multiply parentheses

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

Wy multiply elements

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

We add all the numbers together, and all the variables

6x^2+18x-1=0

a = 6; b = 18; c = -1;
Δ = b2-4ac
Δ = 182-4·6·(-1)
Δ = 348
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:

$\sqrt{\Delta}=\sqrt{348}=\sqrt{4*87}=\sqrt{4}*\sqrt{87}=2\sqrt{87}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{87}}{2*6}=\frac{-18-2\sqrt{87}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{87}}{2*6}=\frac{-18+2\sqrt{87}}{12}
$