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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

6b^2-1080b+3=0

a = 6; b = -1080; c = +3;
Δ = b2-4ac
Δ = -10802-4·6·3
Δ = 1166328
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:

$\sqrt{\Delta}=\sqrt{1166328}=\sqrt{36*32398}=\sqrt{36}*\sqrt{32398}=6\sqrt{32398}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1080)-6\sqrt{32398}}{2*6}=\frac{1080-6\sqrt{32398}}{12}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1080)+6\sqrt{32398}}{2*6}=\frac{1080+6\sqrt{32398}}{12}
$