6x=27-3/2x

Solution for 6x=27-3/2x equation:

6x=27-3/2x

We move all terms to the left:

6x-(27-3/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6x-(-3/2x+27)=0

We get rid of parentheses

6x+3/2x-27=0

We multiply all the terms by the denominator


6x*2x-27*2x+3=0

Wy multiply elements

12x^2-54x+3=0

a = 12; b = -54; c = +3;
Δ = b2-4ac
Δ = -542-4·12·3
Δ = 2772
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:

$\sqrt{\Delta}=\sqrt{2772}=\sqrt{36*77}=\sqrt{36}*\sqrt{77}=6\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{77}}{2*12}=\frac{54-6\sqrt{77}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{77}}{2*12}=\frac{54+6\sqrt{77}}{24}
$