b+(b+15)+90+(2b-90)+3/2b=540

Solution for b+(b+15)+90+(2b-90)+3/2b=540 equation:

b+(b+15)+90+(2b-90)+3/2b=540

We move all terms to the left:

b+(b+15)+90+(2b-90)+3/2b-(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

b+(b+15)+(2b-90)+3/2b-450=0

We get rid of parentheses

b+b+2b+3/2b+15-90-450=0

We multiply all the terms by the denominator


b*2b+b*2b+2b*2b+15*2b-90*2b-450*2b+3=0

Wy multiply elements

2b^2+2b^2+4b^2+30b-180b-900b+3=0

We add all the numbers together, and all the variables

8b^2-1050b+3=0

a = 8; b = -1050; c = +3;
Δ = b2-4ac
Δ = -10502-4·8·3
Δ = 1102404
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:

$\sqrt{\Delta}=\sqrt{1102404}=\sqrt{4*275601}=\sqrt{4}*\sqrt{275601}=2\sqrt{275601}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1050)-2\sqrt{275601}}{2*8}=\frac{1050-2\sqrt{275601}}{16}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1050)+2\sqrt{275601}}{2*8}=\frac{1050+2\sqrt{275601}}{16}
$