B+3/2b+b+45+2b-90+90=180

Solution for B+3/2b+b+45+2b-90+90=180 equation:

+3/2B+B+45+2B-90+90=180

We move all terms to the left:

+3/2B+B+45+2B-90+90-(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

3B+3/2B-135=0

We multiply all the terms by the denominator


3B*2B-135*2B+3=0

Wy multiply elements

6B^2-270B+3=0

a = 6; b = -270; c = +3;
Δ = b2-4ac
Δ = -2702-4·6·3
Δ = 72828
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:

$\sqrt{\Delta}=\sqrt{72828}=\sqrt{10404*7}=\sqrt{10404}*\sqrt{7}=102\sqrt{7}$
$B_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-270)-102\sqrt{7}}{2*6}=\frac{270-102\sqrt{7}}{12}
$
$B_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-270)+102\sqrt{7}}{2*6}=\frac{270+102\sqrt{7}}{12}
$