b+(b+15)+90+(2b-90)+3/2b=650

Solution for b+(b+15)+90+(2b-90)+3/2b=650 equation:

b+(b+15)+90+(2b-90)+3/2b=650

We move all terms to the left:

b+(b+15)+90+(2b-90)+3/2b-(650)=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-560=0

We get rid of parentheses

b+b+2b+3/2b+15-90-560=0

We multiply all the terms by the denominator


b*2b+b*2b+2b*2b+15*2b-90*2b-560*2b+3=0

Wy multiply elements

2b^2+2b^2+4b^2+30b-180b-1120b+3=0

We add all the numbers together, and all the variables

8b^2-1270b+3=0

a = 8; b = -1270; c = +3;
Δ = b2-4ac
Δ = -12702-4·8·3
Δ = 1612804
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:

$\sqrt{\Delta}=\sqrt{1612804}=\sqrt{4*403201}=\sqrt{4}*\sqrt{403201}=2\sqrt{403201}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1270)-2\sqrt{403201}}{2*8}=\frac{1270-2\sqrt{403201}}{16}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1270)+2\sqrt{403201}}{2*8}=\frac{1270+2\sqrt{403201}}{16}
$