20x=1/2x-6

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

20x=1/2x-6

We move all terms to the left:

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


Domain of the equation: 2x-6)!=0

x∈R


We get rid of parentheses

20x-1/2x+6=0

We multiply all the terms by the denominator


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

Wy multiply elements

40x^2+12x-1=0

a = 40; b = 12; c = -1;
Δ = b2-4ac
Δ = 122-4·40·(-1)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{19}}{2*40}=\frac{-12-4\sqrt{19}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{19}}{2*40}=\frac{-12+4\sqrt{19}}{80}
$