(2B-90)+90(b+45)+b+11/2b=540

Solution for (2B-90)+90(b+45)+b+11/2b=540 equation:

(2-90)+90(B+45)+B+11/2B=540

We move all terms to the left:

(2-90)+90(B+45)+B+11/2B-(540)=0


Domain of the equation: 2B!=0

B!=0/2

B!=0

B∈R


determiningTheFunctionDomain
90(B+45)+B+11/2B-540+(2-90)=0

We add all the numbers together, and all the variables

90(B+45)+B+11/2B-540+(-88)=0

We add all the numbers together, and all the variables

B+90(B+45)+11/2B-628=0

We multiply parentheses

B+90B+11/2B+4050-628=0

We multiply all the terms by the denominator


B*2B+90B*2B+4050*2B-628*2B+11=0

Wy multiply elements

2B^2+180B^2+8100B-1256B+11=0

We add all the numbers together, and all the variables

182B^2+6844B+11=0

a = 182; b = 6844; c = +11;
Δ = b2-4ac
Δ = 68442-4·182·11
Δ = 46832328
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:

$\sqrt{\Delta}=\sqrt{46832328}=\sqrt{36*1300898}=\sqrt{36}*\sqrt{1300898}=6\sqrt{1300898}$
$B_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6844)-6\sqrt{1300898}}{2*182}=\frac{-6844-6\sqrt{1300898}}{364}
$
$B_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6844)+6\sqrt{1300898}}{2*182}=\frac{-6844+6\sqrt{1300898}}{364}
$