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

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

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

We move all terms to the left:

(b+45)+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+45)+(2b-90)+3/2b-450=0

We get rid of parentheses

b+2b+3/2b+45-90-450=0

We multiply all the terms by the denominator


b*2b+2b*2b+45*2b-90*2b-450*2b+3=0

Wy multiply elements

2b^2+4b^2+90b-180b-900b+3=0

We add all the numbers together, and all the variables

6b^2-990b+3=0

a = 6; b = -990; c = +3;
Δ = b2-4ac
Δ = -9902-4·6·3
Δ = 980028
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:

$\sqrt{\Delta}=\sqrt{980028}=\sqrt{36*27223}=\sqrt{36}*\sqrt{27223}=6\sqrt{27223}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-990)-6\sqrt{27223}}{2*6}=\frac{990-6\sqrt{27223}}{12}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-990)+6\sqrt{27223}}{2*6}=\frac{990+6\sqrt{27223}}{12}
$