3x+3/2x+2x+3x+x=180

Solution for 3x+3/2x+2x+3x+x=180 equation:

3x+3/2x+2x+3x+x=180

We move all terms to the left:

3x+3/2x+2x+3x+x-(180)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

9x+3/2x-180=0

We multiply all the terms by the denominator


9x*2x-180*2x+3=0

Wy multiply elements

18x^2-360x+3=0

a = 18; b = -360; c = +3;
Δ = b2-4ac
Δ = -3602-4·18·3
Δ = 129384
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:

$\sqrt{\Delta}=\sqrt{129384}=\sqrt{36*3594}=\sqrt{36}*\sqrt{3594}=6\sqrt{3594}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-6\sqrt{3594}}{2*18}=\frac{360-6\sqrt{3594}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+6\sqrt{3594}}{2*18}=\frac{360+6\sqrt{3594}}{36}
$