3x+4/x-2=-4x+12/x-2

Solution for 3x+4/x-2=-4x+12/x-2 equation:

3x+4/x-2=-4x+12/x-2

We move all terms to the left:

3x+4/x-2-(-4x+12/x-2)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

3x+4/x+4x-12/x+2-2=0

We multiply all the terms by the denominator


3x*x+4x*x+2*x-2*x+4-12=0

We add all the numbers together, and all the variables

3x*x+4x*x-8=0

Wy multiply elements

3x^2+4x^2-8=0

We add all the numbers together, and all the variables

7x^2-8=0

a = 7; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·7·(-8)
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{14}}{2*7}=\frac{0-4\sqrt{14}}{14}
=-\frac{4\sqrt{14}}{14}
=-\frac{2\sqrt{14}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{14}}{2*7}=\frac{0+4\sqrt{14}}{14}
=\frac{4\sqrt{14}}{14}
=\frac{2\sqrt{14}}{7}
$