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

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

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

We move all terms to the left:

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


Domain of the equation: b!=0

b∈R


We add all the numbers together, and all the variables

b+3/b+(b+45)+(2b-90)-450=0

We get rid of parentheses

b+3/b+b+2b+45-90-450=0

We multiply all the terms by the denominator


b*b+b*b+2b*b+45*b-90*b-450*b+3=0

We add all the numbers together, and all the variables

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

Wy multiply elements

b^2+b^2+2b^2-495b+3=0

We add all the numbers together, and all the variables

4b^2-495b+3=0

a = 4; b = -495; c = +3;
Δ = b2-4ac
Δ = -4952-4·4·3
Δ = 244977
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-495)-\sqrt{244977}}{2*4}=\frac{495-\sqrt{244977}}{8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-495)+\sqrt{244977}}{2*4}=\frac{495+\sqrt{244977}}{8}
$