32=112/x-2x

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Solution for 32=112/x-2x equation:



32=112/x-2x
We move all terms to the left:
32-(112/x-2x)=0
Domain of the equation: x-2x)!=0
x∈R
We add all the numbers together, and all the variables
-(-2x+112/x)+32=0
We get rid of parentheses
2x-112/x+32=0
We multiply all the terms by the denominator
2x*x+32*x-112=0
We add all the numbers together, and all the variables
32x+2x*x-112=0
Wy multiply elements
2x^2+32x-112=0
a = 2; b = 32; c = -112;
Δ = b2-4ac
Δ = 322-4·2·(-112)
Δ = 1920
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:
$\sqrt{\Delta}=\sqrt{1920}=\sqrt{64*30}=\sqrt{64}*\sqrt{30}=8\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-8\sqrt{30}}{2*2}=\frac{-32-8\sqrt{30}}{4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+8\sqrt{30}}{2*2}=\frac{-32+8\sqrt{30}}{4} $

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