1/2x+52+x+44+3x+12=180

Solution for 1/2x+52+x+44+3x+12=180 equation:

1/2x+52+x+44+3x+12=180

We move all terms to the left:

1/2x+52+x+44+3x+12-(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-72=0

We multiply all the terms by the denominator


4x*2x-72*2x+1=0

Wy multiply elements

8x^2-144x+1=0

a = 8; b = -144; c = +1;
Δ = b2-4ac
Δ = -1442-4·8·1
Δ = 20704
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:

$\sqrt{\Delta}=\sqrt{20704}=\sqrt{16*1294}=\sqrt{16}*\sqrt{1294}=4\sqrt{1294}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-4\sqrt{1294}}{2*8}=\frac{144-4\sqrt{1294}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+4\sqrt{1294}}{2*8}=\frac{144+4\sqrt{1294}}{16}
$