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

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

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

We move all terms to the left:

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


Domain of the equation: 2b+b+b+45+2b-90+90)!=0

We move all terms containing b to the left, all other terms to the right

2b+b+b+2b+90)!=45

b∈R


We add all the numbers together, and all the variables

-(4b+3/2b+45)+540=0

We get rid of parentheses

-4b-3/2b-45+540=0

We multiply all the terms by the denominator


-4b*2b-45*2b+540*2b-3=0

Wy multiply elements

-8b^2-90b+1080b-3=0

We add all the numbers together, and all the variables

-8b^2+990b-3=0

a = -8; b = 990; c = -3;
Δ = b2-4ac
Δ = 9902-4·(-8)·(-3)
Δ = 980004
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:

$\sqrt{\Delta}=\sqrt{980004}=\sqrt{4*245001}=\sqrt{4}*\sqrt{245001}=2\sqrt{245001}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(990)-2\sqrt{245001}}{2*-8}=\frac{-990-2\sqrt{245001}}{-16}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(990)+2\sqrt{245001}}{2*-8}=\frac{-990+2\sqrt{245001}}{-16}
$