x+3/x=160

Solution for x+3/x=160 equation:

x+3/x=160

We move all terms to the left:

x+3/x-(160)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


x*x-160*x+3=0

We add all the numbers together, and all the variables

-160x+x*x+3=0

Wy multiply elements

x^2-160x+3=0

a = 1; b = -160; c = +3;
Δ = b2-4ac
Δ = -1602-4·1·3
Δ = 25588
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:

$\sqrt{\Delta}=\sqrt{25588}=\sqrt{4*6397}=\sqrt{4}*\sqrt{6397}=2\sqrt{6397}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-2\sqrt{6397}}{2*1}=\frac{160-2\sqrt{6397}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+2\sqrt{6397}}{2*1}=\frac{160+2\sqrt{6397}}{2}
$