2x-4/3x=120

Solution for 2x-4/3x=120 equation:

2x-4/3x=120

We move all terms to the left:

2x-4/3x-(120)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


2x*3x-120*3x-4=0

Wy multiply elements

6x^2-360x-4=0

a = 6; b = -360; c = -4;
Δ = b2-4ac
Δ = -3602-4·6·(-4)
Δ = 129696
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:

$\sqrt{\Delta}=\sqrt{129696}=\sqrt{16*8106}=\sqrt{16}*\sqrt{8106}=4\sqrt{8106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-4\sqrt{8106}}{2*6}=\frac{360-4\sqrt{8106}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+4\sqrt{8106}}{2*6}=\frac{360+4\sqrt{8106}}{12}
$