2/5x+120=x

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

2/5x+120=x

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+2/5x+120=0

We multiply all the terms by the denominator


-1x*5x+120*5x+2=0

Wy multiply elements

-5x^2+600x+2=0

a = -5; b = 600; c = +2;
Δ = b2-4ac
Δ = 6002-4·(-5)·2
Δ = 360040
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:

$\sqrt{\Delta}=\sqrt{360040}=\sqrt{4*90010}=\sqrt{4}*\sqrt{90010}=2\sqrt{90010}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(600)-2\sqrt{90010}}{2*-5}=\frac{-600-2\sqrt{90010}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(600)+2\sqrt{90010}}{2*-5}=\frac{-600+2\sqrt{90010}}{-10}
$