14/4x-6=14+3x

Solution for 14/4x-6=14+3x equation:

14/4x-6=14+3x

We move all terms to the left:

14/4x-6-(14+3x)=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+14)-6=0

We get rid of parentheses

14/4x-3x-14-6=0

We multiply all the terms by the denominator


-3x*4x-14*4x-6*4x+14=0

Wy multiply elements

-12x^2-56x-24x+14=0

We add all the numbers together, and all the variables

-12x^2-80x+14=0

a = -12; b = -80; c = +14;
Δ = b2-4ac
Δ = -802-4·(-12)·14
Δ = 7072
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:

$\sqrt{\Delta}=\sqrt{7072}=\sqrt{16*442}=\sqrt{16}*\sqrt{442}=4\sqrt{442}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-4\sqrt{442}}{2*-12}=\frac{80-4\sqrt{442}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+4\sqrt{442}}{2*-12}=\frac{80+4\sqrt{442}}{-24}
$