2x+3200/x+3200=0

Solution for 2x+3200/x+3200=0 equation:

2x+3200/x+3200=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


2x*x+3200*x+3200=0

We add all the numbers together, and all the variables

3200x+2x*x+3200=0

Wy multiply elements

2x^2+3200x+3200=0

a = 2; b = 3200; c = +3200;
Δ = b2-4ac
Δ = 32002-4·2·3200
Δ = 10214400
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:

$\sqrt{\Delta}=\sqrt{10214400}=\sqrt{25600*399}=\sqrt{25600}*\sqrt{399}=160\sqrt{399}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3200)-160\sqrt{399}}{2*2}=\frac{-3200-160\sqrt{399}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3200)+160\sqrt{399}}{2*2}=\frac{-3200+160\sqrt{399}}{4}
$