2b+b+(1/2b-2)=180

Solution for 2b+b+(1/2b-2)=180 equation:

2b+b+(1/2b-2)=180

We move all terms to the left:

2b+b+(1/2b-2)-(180)=0


Domain of the equation: 2b-2)!=0

b∈R


We add all the numbers together, and all the variables

3b+(1/2b-2)-180=0

We get rid of parentheses

3b+1/2b-2-180=0

We multiply all the terms by the denominator


3b*2b-2*2b-180*2b+1=0

Wy multiply elements

6b^2-4b-360b+1=0

We add all the numbers together, and all the variables

6b^2-364b+1=0

a = 6; b = -364; c = +1;
Δ = b2-4ac
Δ = -3642-4·6·1
Δ = 132472
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:

$\sqrt{\Delta}=\sqrt{132472}=\sqrt{4*33118}=\sqrt{4}*\sqrt{33118}=2\sqrt{33118}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-364)-2\sqrt{33118}}{2*6}=\frac{364-2\sqrt{33118}}{12}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-364)+2\sqrt{33118}}{2*6}=\frac{364+2\sqrt{33118}}{12}
$