3x+3/2x=90

Solution for 3x+3/2x=90 equation:

3x+3/2x=90

We move all terms to the left:

3x+3/2x-(90)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


3x*2x-90*2x+3=0

Wy multiply elements

6x^2-180x+3=0

a = 6; b = -180; c = +3;
Δ = b2-4ac
Δ = -1802-4·6·3
Δ = 32328
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:

$\sqrt{\Delta}=\sqrt{32328}=\sqrt{36*898}=\sqrt{36}*\sqrt{898}=6\sqrt{898}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-6\sqrt{898}}{2*6}=\frac{180-6\sqrt{898}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+6\sqrt{898}}{2*6}=\frac{180+6\sqrt{898}}{12}
$