120+2/5x=2x

Solution for 120+2/5x=2x equation:

120+2/5x=2x

We move all terms to the left:

120+2/5x-(2x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-2x+2/5x+120=0

We multiply all the terms by the denominator


-2x*5x+120*5x+2=0

Wy multiply elements

-10x^2+600x+2=0

a = -10; b = 600; c = +2;
Δ = b2-4ac
Δ = 6002-4·(-10)·2
Δ = 360080
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:

$\sqrt{\Delta}=\sqrt{360080}=\sqrt{16*22505}=\sqrt{16}*\sqrt{22505}=4\sqrt{22505}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(600)-4\sqrt{22505}}{2*-10}=\frac{-600-4\sqrt{22505}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(600)+4\sqrt{22505}}{2*-10}=\frac{-600+4\sqrt{22505}}{-20}
$