32/x+6x=90

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Solution for 32/x+6x=90 equation:



32/x+6x=90
We move all terms to the left:
32/x+6x-(90)=0
Domain of the equation: x!=0
x∈R
We add all the numbers together, and all the variables
6x+32/x-90=0
We multiply all the terms by the denominator
6x*x-90*x+32=0
We add all the numbers together, and all the variables
-90x+6x*x+32=0
Wy multiply elements
6x^2-90x+32=0
a = 6; b = -90; c = +32;
Δ = b2-4ac
Δ = -902-4·6·32
Δ = 7332
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:
$\sqrt{\Delta}=\sqrt{7332}=\sqrt{4*1833}=\sqrt{4}*\sqrt{1833}=2\sqrt{1833}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{1833}}{2*6}=\frac{90-2\sqrt{1833}}{12} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{1833}}{2*6}=\frac{90+2\sqrt{1833}}{12} $

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