x+1/2x+3x=180

Solution for x+1/2x+3x=180 equation:

x+1/2x+3x=180

We move all terms to the left:

x+1/2x+3x-(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

4x+1/2x-180=0

We multiply all the terms by the denominator


4x*2x-180*2x+1=0

Wy multiply elements

8x^2-360x+1=0

a = 8; b = -360; c = +1;
Δ = b2-4ac
Δ = -3602-4·8·1
Δ = 129568
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:

$\sqrt{\Delta}=\sqrt{129568}=\sqrt{16*8098}=\sqrt{16}*\sqrt{8098}=4\sqrt{8098}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-4\sqrt{8098}}{2*8}=\frac{360-4\sqrt{8098}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+4\sqrt{8098}}{2*8}=\frac{360+4\sqrt{8098}}{16}
$