(b+45)+b(2b-90)+90+1.5b=540

Solution for (b+45)+b(2b-90)+90+1.5b=540 equation:

(b+45)+b(2b-90)+90+1.5b=540

We move all terms to the left:

(b+45)+b(2b-90)+90+1.5b-(540)=0

We add all the numbers together, and all the variables

1.5b+(b+45)+b(2b-90)-450=0

We multiply parentheses

2b^2+1.5b+(b+45)-90b-450=0

We get rid of parentheses

2b^2+1.5b+b-90b+45-450=0

We add all the numbers together, and all the variables

2b^2-87.5b-405=0

a = 2; b = -87.5; c = -405;
Δ = b2-4ac
Δ = -87.52-4·2·(-405)
Δ = 10896.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-87.5)-\sqrt{10896.25}}{2*2}=\frac{87.5-\sqrt{10896.25}}{4}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-87.5)+\sqrt{10896.25}}{2*2}=\frac{87.5+\sqrt{10896.25}}{4}
$