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

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

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

We move all terms to the left:

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


Domain of the equation: 2)b!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3b^2+4b-495=0

a = 3; b = 4; c = -495;
Δ = b2-4ac
Δ = 42-4·3·(-495)
Δ = 5956
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:

$\sqrt{\Delta}=\sqrt{5956}=\sqrt{4*1489}=\sqrt{4}*\sqrt{1489}=2\sqrt{1489}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{1489}}{2*3}=\frac{-4-2\sqrt{1489}}{6}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{1489}}{2*3}=\frac{-4+2\sqrt{1489}}{6}
$