4x+8/x=12

Solution for 4x+8/x=12 equation:

4x+8/x=12

We move all terms to the left:

4x+8/x-(12)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


4x*x-12*x+8=0

We add all the numbers together, and all the variables

-12x+4x*x+8=0

Wy multiply elements

4x^2-12x+8=0

a = 4; b = -12; c = +8;
Δ = b2-4ac
Δ = -122-4·4·8
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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