B(b+450)+90(2b-90)+3/2b=540

Solution for B(b+450)+90(2b-90)+3/2b=540 equation:

(B+450)+90(2B-90)+3/2B=540

We move all terms to the left:

(B+450)+90(2B-90)+3/2B-(540)=0


Domain of the equation: 2B!=0

B!=0/2

B!=0

B∈R


We multiply parentheses

(B+450)+180B+3/2B-8100-540=0

We get rid of parentheses

B+180B+3/2B+450-8100-540=0

We multiply all the terms by the denominator


B*2B+180B*2B+450*2B-8100*2B-540*2B+3=0

Wy multiply elements

2B^2+360B^2+900B-16200B-1080B+3=0

We add all the numbers together, and all the variables

362B^2-16380B+3=0

a = 362; b = -16380; c = +3;
Δ = b2-4ac
Δ = -163802-4·362·3
Δ = 268300056
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:

$\sqrt{\Delta}=\sqrt{268300056}=\sqrt{4*67075014}=\sqrt{4}*\sqrt{67075014}=2\sqrt{67075014}$
$B_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16380)-2\sqrt{67075014}}{2*362}=\frac{16380-2\sqrt{67075014}}{724}
$
$B_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16380)+2\sqrt{67075014}}{2*362}=\frac{16380+2\sqrt{67075014}}{724}
$