-1/2x+6x=20

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

-1/2x+6x=20

We move all terms to the left:

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

We multiply all the terms by the denominator


6x*2x-20*2x-1=0

Wy multiply elements

12x^2-40x-1=0

a = 12; b = -40; c = -1;
Δ = b2-4ac
Δ = -402-4·12·(-1)
Δ = 1648
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:

$\sqrt{\Delta}=\sqrt{1648}=\sqrt{16*103}=\sqrt{16}*\sqrt{103}=4\sqrt{103}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{103}}{2*12}=\frac{40-4\sqrt{103}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{103}}{2*12}=\frac{40+4\sqrt{103}}{24}
$