-1/2x+6x+2=20

Solution for -1/2x+6x+2=20 equation:

-1/2x+6x+2=20

We move all terms to the left:

-1/2x+6x+2-(20)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

6x-1/2x-18=0

We multiply all the terms by the denominator


6x*2x-18*2x-1=0

Wy multiply elements

12x^2-36x-1=0

a = 12; b = -36; c = -1;
Δ = b2-4ac
Δ = -362-4·12·(-1)
Δ = 1344
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:

$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-8\sqrt{21}}{2*12}=\frac{36-8\sqrt{21}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+8\sqrt{21}}{2*12}=\frac{36+8\sqrt{21}}{24}
$