3x+6-1/2x=-4

Solution for 3x+6-1/2x=-4 equation:

3x+6-1/2x=-4

We move all terms to the left:

3x+6-1/2x-(-4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3x-1/2x+10=0

We multiply all the terms by the denominator


3x*2x+10*2x-1=0

Wy multiply elements

6x^2+20x-1=0

a = 6; b = 20; c = -1;
Δ = b2-4ac
Δ = 202-4·6·(-1)
Δ = 424
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:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{106}}{2*6}=\frac{-20-2\sqrt{106}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{106}}{2*6}=\frac{-20+2\sqrt{106}}{12}
$