2x+56/3x=56

Solution for 2x+56/3x=56 equation:

2x+56/3x=56

We move all terms to the left:

2x+56/3x-(56)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


2x*3x-56*3x+56=0

Wy multiply elements

6x^2-168x+56=0

a = 6; b = -168; c = +56;
Δ = b2-4ac
Δ = -1682-4·6·56
Δ = 26880
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:

$\sqrt{\Delta}=\sqrt{26880}=\sqrt{256*105}=\sqrt{256}*\sqrt{105}=16\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-168)-16\sqrt{105}}{2*6}=\frac{168-16\sqrt{105}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-168)+16\sqrt{105}}{2*6}=\frac{168+16\sqrt{105}}{12}
$