14/4x+2/2=3x-4

Solution for 14/4x+2/2=3x-4 equation:

14/4x+2/2=3x-4

We move all terms to the left:

14/4x+2/2-(3x-4)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

14/4x-(3x-4)+1=0

We get rid of parentheses

14/4x-3x+4+1=0

We multiply all the terms by the denominator


-3x*4x+4*4x+1*4x+14=0

Wy multiply elements

-12x^2+16x+4x+14=0

We add all the numbers together, and all the variables

-12x^2+20x+14=0

a = -12; b = 20; c = +14;
Δ = b2-4ac
Δ = 202-4·(-12)·14
Δ = 1072
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:

$\sqrt{\Delta}=\sqrt{1072}=\sqrt{16*67}=\sqrt{16}*\sqrt{67}=4\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{67}}{2*-12}=\frac{-20-4\sqrt{67}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{67}}{2*-12}=\frac{-20+4\sqrt{67}}{-24}
$