27+6x=81/4x

Solution for 27+6x=81/4x equation:

27+6x=81/4x

We move all terms to the left:

27+6x-(81/4x)=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-(+81/4x)+27=0

We get rid of parentheses

6x-81/4x+27=0

We multiply all the terms by the denominator


6x*4x+27*4x-81=0

Wy multiply elements

24x^2+108x-81=0

a = 24; b = 108; c = -81;
Δ = b2-4ac
Δ = 1082-4·24·(-81)
Δ = 19440
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:

$\sqrt{\Delta}=\sqrt{19440}=\sqrt{1296*15}=\sqrt{1296}*\sqrt{15}=36\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-36\sqrt{15}}{2*24}=\frac{-108-36\sqrt{15}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+36\sqrt{15}}{2*24}=\frac{-108+36\sqrt{15}}{48}
$