3x+3/2x=27

Solution for 3x+3/2x=27 equation:

3x+3/2x=27

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

6x^2-54x+3=0

a = 6; b = -54; c = +3;
Δ = b2-4ac
Δ = -542-4·6·3
Δ = 2844
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:

$\sqrt{\Delta}=\sqrt{2844}=\sqrt{36*79}=\sqrt{36}*\sqrt{79}=6\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{79}}{2*6}=\frac{54-6\sqrt{79}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{79}}{2*6}=\frac{54+6\sqrt{79}}{12}
$