6x=5+1/4x

Solution for 6x=5+1/4x equation:

6x=5+1/4x

We move all terms to the left:

6x-(5+1/4x)=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-(1/4x+5)=0

We get rid of parentheses

6x-1/4x-5=0

We multiply all the terms by the denominator


6x*4x-5*4x-1=0

Wy multiply elements

24x^2-20x-1=0

a = 24; b = -20; c = -1;
Δ = b2-4ac
Δ = -202-4·24·(-1)
Δ = 496
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:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{31}}{2*24}=\frac{20-4\sqrt{31}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{31}}{2*24}=\frac{20+4\sqrt{31}}{48}
$