3x+16/x=26

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Solution for 3x+16/x=26 equation:



3x+16/x=26
We move all terms to the left:
3x+16/x-(26)=0
Domain of the equation: x!=0
x∈R
We multiply all the terms by the denominator
3x*x-26*x+16=0
We add all the numbers together, and all the variables
-26x+3x*x+16=0
Wy multiply elements
3x^2-26x+16=0
a = 3; b = -26; c = +16;
Δ = b2-4ac
Δ = -262-4·3·16
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-22}{2*3}=\frac{4}{6} =2/3 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+22}{2*3}=\frac{48}{6} =8 $

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