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

Solution for 90+(2b-90)+(3/2)b+(b+45)+b=450 equation:

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

We move all terms to the left:

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

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

We add all the numbers together, and all the variables

b+(2b-90)+(+3/2)b+(b+45)-360=0

We multiply parentheses

3b^2+b+(2b-90)+(b+45)-360=0

We get rid of parentheses

3b^2+b+2b+b-90+45-360=0

We add all the numbers together, and all the variables

3b^2+4b-405=0

a = 3; b = 4; c = -405;
Δ = b2-4ac
Δ = 42-4·3·(-405)
Δ = 4876
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:

$\sqrt{\Delta}=\sqrt{4876}=\sqrt{4*1219}=\sqrt{4}*\sqrt{1219}=2\sqrt{1219}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{1219}}{2*3}=\frac{-4-2\sqrt{1219}}{6}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{1219}}{2*3}=\frac{-4+2\sqrt{1219}}{6}
$