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

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

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

We move all terms to the left:

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

3/2B+(B+45)-(2B-90)-90=0

We get rid of parentheses

3/2B+B-2B+45+90-90=0

We multiply all the terms by the denominator


B*2B-2B*2B+45*2B+90*2B-90*2B+3=0

Wy multiply elements

2B^2-4B^2+90B+180B-180B+3=0

We add all the numbers together, and all the variables

-2B^2+90B+3=0

a = -2; b = 90; c = +3;
Δ = b2-4ac
Δ = 902-4·(-2)·3
Δ = 8124
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:

$\sqrt{\Delta}=\sqrt{8124}=\sqrt{4*2031}=\sqrt{4}*\sqrt{2031}=2\sqrt{2031}$
$B_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-2\sqrt{2031}}{2*-2}=\frac{-90-2\sqrt{2031}}{-4}
$
$B_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+2\sqrt{2031}}{2*-2}=\frac{-90+2\sqrt{2031}}{-4}
$