4x/12+5x/x=8

Solution for 4x/12+5x/x=8 equation:

4x/12+5x/x=8

We move all terms to the left:

4x/12+5x/x-(8)=0


Domain of the equation: x!=0

x∈R


We calculate fractions


4x^2/12x+60x/12x-8=0

We multiply all the terms by the denominator


4x^2+60x-8*12x=0

Wy multiply elements

4x^2+60x-96x=0

We add all the numbers together, and all the variables

4x^2-36x=0

a = 4; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·4·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*4}=\frac{72}{8}
=9
$