13x+(16/8x)=26

Solution for 13x+(16/8x)=26 equation:

13x+(16/8x)=26

We move all terms to the left:

13x+(16/8x)-(26)=0


Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

13x+(+16/8x)-26=0

We get rid of parentheses

13x+16/8x-26=0

We multiply all the terms by the denominator


13x*8x-26*8x+16=0

Wy multiply elements

104x^2-208x+16=0

a = 104; b = -208; c = +16;
Δ = b2-4ac
Δ = -2082-4·104·16
Δ = 36608
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:

$\sqrt{\Delta}=\sqrt{36608}=\sqrt{256*143}=\sqrt{256}*\sqrt{143}=16\sqrt{143}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-208)-16\sqrt{143}}{2*104}=\frac{208-16\sqrt{143}}{208}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-208)+16\sqrt{143}}{2*104}=\frac{208+16\sqrt{143}}{208}
$