x-16+2x+43+1/2x+8=180

Solution for x-16+2x+43+1/2x+8=180 equation:

x-16+2x+43+1/2x+8=180

We move all terms to the left:

x-16+2x+43+1/2x+8-(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+1/2x-145=0

We multiply all the terms by the denominator


3x*2x-145*2x+1=0

Wy multiply elements

6x^2-290x+1=0

a = 6; b = -290; c = +1;
Δ = b2-4ac
Δ = -2902-4·6·1
Δ = 84076
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:

$\sqrt{\Delta}=\sqrt{84076}=\sqrt{4*21019}=\sqrt{4}*\sqrt{21019}=2\sqrt{21019}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-290)-2\sqrt{21019}}{2*6}=\frac{290-2\sqrt{21019}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-290)+2\sqrt{21019}}{2*6}=\frac{290+2\sqrt{21019}}{12}
$