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

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

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

We move all terms to the left:

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


Domain of the equation: 2B!=0

B!=0/2

B!=0

B∈R


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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

B+(2B-90)+3/2B-405=0

We get rid of parentheses

B+2B+3/2B-90-405=0

We multiply all the terms by the denominator


B*2B+2B*2B-90*2B-405*2B+3=0

Wy multiply elements

2B^2+4B^2-180B-810B+3=0

We add all the numbers together, and all the variables

6B^2-990B+3=0

a = 6; b = -990; c = +3;
Δ = b2-4ac
Δ = -9902-4·6·3
Δ = 980028
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:

$\sqrt{\Delta}=\sqrt{980028}=\sqrt{36*27223}=\sqrt{36}*\sqrt{27223}=6\sqrt{27223}$
$B_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-990)-6\sqrt{27223}}{2*6}=\frac{990-6\sqrt{27223}}{12}
$
$B_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-990)+6\sqrt{27223}}{2*6}=\frac{990+6\sqrt{27223}}{12}
$