x+5/8x=26

Solution for x+5/8x=26 equation:

x+5/8x=26

We move all terms to the left:

x+5/8x-(26)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We multiply all the terms by the denominator


x*8x-26*8x+5=0

Wy multiply elements

8x^2-208x+5=0

a = 8; b = -208; c = +5;
Δ = b2-4ac
Δ = -2082-4·8·5
Δ = 43104
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:

$\sqrt{\Delta}=\sqrt{43104}=\sqrt{16*2694}=\sqrt{16}*\sqrt{2694}=4\sqrt{2694}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-208)-4\sqrt{2694}}{2*8}=\frac{208-4\sqrt{2694}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-208)+4\sqrt{2694}}{2*8}=\frac{208+4\sqrt{2694}}{16}
$