2x+x+3/2x+45=180

Solution for 2x+x+3/2x+45=180 equation:

2x+x+3/2x+45=180

We move all terms to the left:

2x+x+3/2x+45-(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-135=0

We multiply all the terms by the denominator


3x*2x-135*2x+3=0

Wy multiply elements

6x^2-270x+3=0

a = 6; b = -270; c = +3;
Δ = b2-4ac
Δ = -2702-4·6·3
Δ = 72828
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:

$\sqrt{\Delta}=\sqrt{72828}=\sqrt{10404*7}=\sqrt{10404}*\sqrt{7}=102\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-270)-102\sqrt{7}}{2*6}=\frac{270-102\sqrt{7}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-270)+102\sqrt{7}}{2*6}=\frac{270+102\sqrt{7}}{12}
$