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

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

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

We move all terms to the left:

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


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

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

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

b∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-6b^2-90b+1080b-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}
$