48/(4x)+48/(3x)=14

Solution for 48/(4x)+48/(3x)=14 equation:

48/(4x)+48/(3x)=14

We move all terms to the left:

48/(4x)+48/(3x)-(14)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


144x/12x^2+192x/12x^2-14=0

We multiply all the terms by the denominator


144x+192x-14*12x^2=0

We add all the numbers together, and all the variables

336x-14*12x^2=0

Wy multiply elements

-168x^2+336x=0

a = -168; b = 336; c = 0;
Δ = b2-4ac
Δ = 3362-4·(-168)·0
Δ = 112896
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{112896}=336$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(336)-336}{2*-168}=\frac{-672}{-336}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(336)+336}{2*-168}=\frac{0}{-336}
=0
$