180x-360/x=160

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Solution for 180x-360/x=160 equation: 



180x-360/x=160

We move all terms to the left:

180x-360/x-(160)=0



Domain of the equation: x!=0

x∈R



We multiply all the terms by the denominator


180x*x-160*x-360=0

We add all the numbers together, and all the variables

-160x+180x*x-360=0

Wy multiply elements

180x^2-160x-360=0

a = 180; b = -160; c = -360;
Δ = b2-4ac
Δ = -1602-4·180·(-360)
Δ = 284800
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:


$\sqrt{\Delta}=\sqrt{284800}=\sqrt{1600*178}=\sqrt{1600}*\sqrt{178}=40\sqrt{178}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-40\sqrt{178}}{2*180}=\frac{160-40\sqrt{178}}{360}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+40\sqrt{178}}{2*180}=\frac{160+40\sqrt{178}}{360}
$

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