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

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

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

We move all terms to the left:

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


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

6b^2+2b^2+90b+3=0

We add all the numbers together, and all the variables

8b^2+90b+3=0

a = 8; b = 90; c = +3;
Δ = b2-4ac
Δ = 902-4·8·3
Δ = 8004
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:

$\sqrt{\Delta}=\sqrt{8004}=\sqrt{4*2001}=\sqrt{4}*\sqrt{2001}=2\sqrt{2001}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-2\sqrt{2001}}{2*8}=\frac{-90-2\sqrt{2001}}{16}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+2\sqrt{2001}}{2*8}=\frac{-90+2\sqrt{2001}}{16}
$