3x+16/x=26

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
$