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

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

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

We move all terms to the left:

2x+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

8x+3/2x-180=0

We multiply all the terms by the denominator


8x*2x-180*2x+3=0

Wy multiply elements

16x^2-360x+3=0

a = 16; b = -360; c = +3;
Δ = b2-4ac
Δ = -3602-4·16·3
Δ = 129408
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:

$\sqrt{\Delta}=\sqrt{129408}=\sqrt{64*2022}=\sqrt{64}*\sqrt{2022}=8\sqrt{2022}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-8\sqrt{2022}}{2*16}=\frac{360-8\sqrt{2022}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+8\sqrt{2022}}{2*16}=\frac{360+8\sqrt{2022}}{32}
$