(80/x)+2x=26

Solution for (80/x)+2x=26 equation:

(80/x)+2x=26

We move all terms to the left:

(80/x)+2x-(26)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+80/x)+2x-26=0

We add all the numbers together, and all the variables

2x+(+80/x)-26=0

We get rid of parentheses

2x+80/x-26=0

We multiply all the terms by the denominator


2x*x-26*x+80=0

We add all the numbers together, and all the variables

-26x+2x*x+80=0

Wy multiply elements

2x^2-26x+80=0

a = 2; b = -26; c = +80;
Δ = b2-4ac
Δ = -262-4·2·80
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-6}{2*2}=\frac{20}{4}
=5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+6}{2*2}=\frac{32}{4}
=8
$