2x+x+3/2x+90+3/2x=360

Solution for 2x+x+3/2x+90+3/2x=360 equation:

2x+x+3/2x+90+3/2x=360

We move all terms to the left:

2x+x+3/2x+90+3/2x-(360)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3x+3/2x+3/2x-270=0

We multiply all the terms by the denominator


3x*2x-270*2x+3+3=0

We add all the numbers together, and all the variables

3x*2x-270*2x+6=0

Wy multiply elements

6x^2-540x+6=0

a = 6; b = -540; c = +6;
Δ = b2-4ac
Δ = -5402-4·6·6
Δ = 291456
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:

$\sqrt{\Delta}=\sqrt{291456}=\sqrt{576*506}=\sqrt{576}*\sqrt{506}=24\sqrt{506}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-24\sqrt{506}}{2*6}=\frac{540-24\sqrt{506}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+24\sqrt{506}}{2*6}=\frac{540+24\sqrt{506}}{12}
$