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

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

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

We move all terms to the left:

b+3/2b-90+90+b+45-(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+3/2b-135=0

We multiply all the terms by the denominator


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

Wy multiply elements

4b^2-270b+3=0

a = 4; b = -270; c = +3;
Δ = b2-4ac
Δ = -2702-4·4·3
Δ = 72852
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:

$\sqrt{\Delta}=\sqrt{72852}=\sqrt{4*18213}=\sqrt{4}*\sqrt{18213}=2\sqrt{18213}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-270)-2\sqrt{18213}}{2*4}=\frac{270-2\sqrt{18213}}{8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-270)+2\sqrt{18213}}{2*4}=\frac{270+2\sqrt{18213}}{8}
$