45+6x+3/2x=180

Solution for 45+6x+3/2x=180 equation:

45+6x+3/2x=180

We move all terms to the left:

45+6x+3/2x-(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

6x+3/2x-135=0

We multiply all the terms by the denominator


6x*2x-135*2x+3=0

Wy multiply elements

12x^2-270x+3=0

a = 12; b = -270; c = +3;
Δ = b2-4ac
Δ = -2702-4·12·3
Δ = 72756
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:

$\sqrt{\Delta}=\sqrt{72756}=\sqrt{36*2021}=\sqrt{36}*\sqrt{2021}=6\sqrt{2021}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-270)-6\sqrt{2021}}{2*12}=\frac{270-6\sqrt{2021}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-270)+6\sqrt{2021}}{2*12}=\frac{270+6\sqrt{2021}}{24}
$