32/x+6x=90

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}
$