x-30+3/2x+2x=180

Solution for x-30+3/2x+2x=180 equation:

x-30+3/2x+2x=180

We move all terms to the left:

x-30+3/2x+2x-(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

3x+3/2x-210=0

We multiply all the terms by the denominator


3x*2x-210*2x+3=0

Wy multiply elements

6x^2-420x+3=0

a = 6; b = -420; c = +3;
Δ = b2-4ac
Δ = -4202-4·6·3
Δ = 176328
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:

$\sqrt{\Delta}=\sqrt{176328}=\sqrt{36*4898}=\sqrt{36}*\sqrt{4898}=6\sqrt{4898}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-420)-6\sqrt{4898}}{2*6}=\frac{420-6\sqrt{4898}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-420)+6\sqrt{4898}}{2*6}=\frac{420+6\sqrt{4898}}{12}
$