B+2/3b+b+2b-90+90+45=540

Solution for B+2/3b+b+2b-90+90+45=540 equation:

+2/3B+B+2B-90+90+45=540

We move all terms to the left:

+2/3B+B+2B-90+90+45-(540)=0


Domain of the equation: 3B!=0

B!=0/3

B!=0

B∈R


We add all the numbers together, and all the variables

3B+2/3B-495=0

We multiply all the terms by the denominator


3B*3B-495*3B+2=0

Wy multiply elements

9B^2-1485B+2=0

a = 9; b = -1485; c = +2;
Δ = b2-4ac
Δ = -14852-4·9·2
Δ = 2205153
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:

$\sqrt{\Delta}=\sqrt{2205153}=\sqrt{9*245017}=\sqrt{9}*\sqrt{245017}=3\sqrt{245017}$
$B_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1485)-3\sqrt{245017}}{2*9}=\frac{1485-3\sqrt{245017}}{18}
$
$B_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1485)+3\sqrt{245017}}{2*9}=\frac{1485+3\sqrt{245017}}{18}
$