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

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

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

We move all terms to the left:

b+3b/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

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

8b^2-267b=0

a = 8; b = -267; c = 0;
Δ = b2-4ac
Δ = -2672-4·8·0
Δ = 71289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{71289}=267$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-267)-267}{2*8}=\frac{0}{16}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-267)+267}{2*8}=\frac{534}{16}
=33+3/8
$