b+3/2b+(b+45)+(25-90)+90=540

Solution for b+3/2b+(b+45)+(25-90)+90=540 equation:

b+3/2b+(b+45)+(25-90)+90=540

We move all terms to the left:

b+3/2b+(b+45)+(25-90)+90-(540)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


determiningTheFunctionDomain
b+3/2b+(b+45)+90-540+(25-90)=0

We add all the numbers together, and all the variables

b+3/2b+(b+45)+90-540+(-65)=0

We add all the numbers together, and all the variables

b+3/2b+(b+45)-515=0

We get rid of parentheses

b+3/2b+b+45-515=0

We multiply all the terms by the denominator


b*2b+b*2b+45*2b-515*2b+3=0

Wy multiply elements

2b^2+2b^2+90b-1030b+3=0

We add all the numbers together, and all the variables

4b^2-940b+3=0

a = 4; b = -940; c = +3;
Δ = b2-4ac
Δ = -9402-4·4·3
Δ = 883552
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:

$\sqrt{\Delta}=\sqrt{883552}=\sqrt{16*55222}=\sqrt{16}*\sqrt{55222}=4\sqrt{55222}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-940)-4\sqrt{55222}}{2*4}=\frac{940-4\sqrt{55222}}{8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-940)+4\sqrt{55222}}{2*4}=\frac{940+4\sqrt{55222}}{8}
$