2x+2/5x=240

Solution for 2x+2/5x=240 equation:

2x+2/5x=240

We move all terms to the left:

2x+2/5x-(240)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


2x*5x-240*5x+2=0

Wy multiply elements

10x^2-1200x+2=0

a = 10; b = -1200; c = +2;
Δ = b2-4ac
Δ = -12002-4·10·2
Δ = 1439920
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:

$\sqrt{\Delta}=\sqrt{1439920}=\sqrt{16*89995}=\sqrt{16}*\sqrt{89995}=4\sqrt{89995}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1200)-4\sqrt{89995}}{2*10}=\frac{1200-4\sqrt{89995}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1200)+4\sqrt{89995}}{2*10}=\frac{1200+4\sqrt{89995}}{20}
$