2x+4/3x=20

Solution for 2x+4/3x=20 equation:

2x+4/3x=20

We move all terms to the left:

2x+4/3x-(20)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


2x*3x-20*3x+4=0

Wy multiply elements

6x^2-60x+4=0

a = 6; b = -60; c = +4;
Δ = b2-4ac
Δ = -602-4·6·4
Δ = 3504
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:

$\sqrt{\Delta}=\sqrt{3504}=\sqrt{16*219}=\sqrt{16}*\sqrt{219}=4\sqrt{219}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{219}}{2*6}=\frac{60-4\sqrt{219}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{219}}{2*6}=\frac{60+4\sqrt{219}}{12}
$