2x+3*2/5x=288

Solution for 2x+3*2/5x=288 equation:

2x+3*2/5x=288

We move all terms to the left:

2x+3*2/5x-(288)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


2x*5x-288*5x+3*2=0

We add all the numbers together, and all the variables

2x*5x-288*5x+6=0

Wy multiply elements

10x^2-1440x+6=0

a = 10; b = -1440; c = +6;
Δ = b2-4ac
Δ = -14402-4·10·6
Δ = 2073360
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:

$\sqrt{\Delta}=\sqrt{2073360}=\sqrt{16*129585}=\sqrt{16}*\sqrt{129585}=4\sqrt{129585}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1440)-4\sqrt{129585}}{2*10}=\frac{1440-4\sqrt{129585}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1440)+4\sqrt{129585}}{2*10}=\frac{1440+4\sqrt{129585}}{20}
$