4x+4/x-2=10

Solution for 4x+4/x-2=10 equation:

4x+4/x-2=10

We move all terms to the left:

4x+4/x-2-(10)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

4x+4/x-12=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

4x^2-12x+4=0

a = 4; b = -12; c = +4;
Δ = b2-4ac
Δ = -122-4·4·4
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{5}}{2*4}=\frac{12-4\sqrt{5}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{5}}{2*4}=\frac{12+4\sqrt{5}}{8}
$