1/2b+27+b-23=180

Solution for 1/2b+27+b-23=180 equation:

1/2b+27+b-23=180

We move all terms to the left:

1/2b+27+b-23-(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

b+1/2b-176=0

We multiply all the terms by the denominator


b*2b-176*2b+1=0

Wy multiply elements

2b^2-352b+1=0

a = 2; b = -352; c = +1;
Δ = b2-4ac
Δ = -3522-4·2·1
Δ = 123896
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:

$\sqrt{\Delta}=\sqrt{123896}=\sqrt{4*30974}=\sqrt{4}*\sqrt{30974}=2\sqrt{30974}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-352)-2\sqrt{30974}}{2*2}=\frac{352-2\sqrt{30974}}{4}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-352)+2\sqrt{30974}}{2*2}=\frac{352+2\sqrt{30974}}{4}
$