x+5/8x=6+x/8x+3

Solution for x+5/8x=6+x/8x+3 equation:

x+5/8x=6+x/8x+3

We move all terms to the left:

x+5/8x-(6+x/8x+3)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 8x+3)!=0

x∈R


We add all the numbers together, and all the variables

x+5/8x-(x/8x+9)=0

We get rid of parentheses

x+5/8x-x/8x-9=0

We multiply all the terms by the denominator


x*8x-x-9*8x+5=0

We add all the numbers together, and all the variables

-1x+x*8x-9*8x+5=0

Wy multiply elements

8x^2-1x-72x+5=0

We add all the numbers together, and all the variables

8x^2-73x+5=0

a = 8; b = -73; c = +5;
Δ = b2-4ac
Δ = -732-4·8·5
Δ = 5169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-73)-\sqrt{5169}}{2*8}=\frac{73-\sqrt{5169}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-73)+\sqrt{5169}}{2*8}=\frac{73+\sqrt{5169}}{16}
$