14/6x+2/2=2x-4

Solution for 14/6x+2/2=2x-4 equation:

14/6x+2/2=2x-4

We move all terms to the left:

14/6x+2/2-(2x-4)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

14/6x-(2x-4)+1=0

We get rid of parentheses

14/6x-2x+4+1=0

We multiply all the terms by the denominator


-2x*6x+4*6x+1*6x+14=0

Wy multiply elements

-12x^2+24x+6x+14=0

We add all the numbers together, and all the variables

-12x^2+30x+14=0

a = -12; b = 30; c = +14;
Δ = b2-4ac
Δ = 302-4·(-12)·14
Δ = 1572
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:

$\sqrt{\Delta}=\sqrt{1572}=\sqrt{4*393}=\sqrt{4}*\sqrt{393}=2\sqrt{393}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{393}}{2*-12}=\frac{-30-2\sqrt{393}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{393}}{2*-12}=\frac{-30+2\sqrt{393}}{-24}
$