5x+8+3x=26/6x

Solution for 5x+8+3x=26/6x equation:

5x+8+3x=26/6x

We move all terms to the left:

5x+8+3x-(26/6x)=0


Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x+3x-(+26/6x)+8=0

We add all the numbers together, and all the variables

8x-(+26/6x)+8=0

We get rid of parentheses

8x-26/6x+8=0

We multiply all the terms by the denominator


8x*6x+8*6x-26=0

Wy multiply elements

48x^2+48x-26=0

a = 48; b = 48; c = -26;
Δ = b2-4ac
Δ = 482-4·48·(-26)
Δ = 7296
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:

$\sqrt{\Delta}=\sqrt{7296}=\sqrt{64*114}=\sqrt{64}*\sqrt{114}=8\sqrt{114}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-8\sqrt{114}}{2*48}=\frac{-48-8\sqrt{114}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+8\sqrt{114}}{2*48}=\frac{-48+8\sqrt{114}}{96}
$