b-18+b+1/2b=180

Solution for b-18+b+1/2b=180 equation:

b-18+b+1/2b=180

We move all terms to the left:

b-18+b+1/2b-(180)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We add all the numbers together, and all the variables

2b+1/2b-198=0

We multiply all the terms by the denominator


2b*2b-198*2b+1=0

Wy multiply elements

4b^2-396b+1=0

a = 4; b = -396; c = +1;
Δ = b2-4ac
Δ = -3962-4·4·1
Δ = 156800
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{156800}=\sqrt{78400*2}=\sqrt{78400}*\sqrt{2}=280\sqrt{2}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-396)-280\sqrt{2}}{2*4}=\frac{396-280\sqrt{2}}{8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-396)+280\sqrt{2}}{2*4}=\frac{396+280\sqrt{2}}{8}
$