6x-26=54/4x

Solution for 6x-26=54/4x equation:

6x-26=54/4x

We move all terms to the left:

6x-26-(54/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6x-(+54/4x)-26=0

We get rid of parentheses

6x-54/4x-26=0

We multiply all the terms by the denominator


6x*4x-26*4x-54=0

Wy multiply elements

24x^2-104x-54=0

a = 24; b = -104; c = -54;
Δ = b2-4ac
Δ = -1042-4·24·(-54)
Δ = 16000
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:

$\sqrt{\Delta}=\sqrt{16000}=\sqrt{1600*10}=\sqrt{1600}*\sqrt{10}=40\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-104)-40\sqrt{10}}{2*24}=\frac{104-40\sqrt{10}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-104)+40\sqrt{10}}{2*24}=\frac{104+40\sqrt{10}}{48}
$