5b+3/2b+45=450

Solution for 5b+3/2b+45=450 equation:

5b+3/2b+45=450

We move all terms to the left:

5b+3/2b+45-(450)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We add all the numbers together, and all the variables

5b+3/2b-405=0

We multiply all the terms by the denominator


5b*2b-405*2b+3=0

Wy multiply elements

10b^2-810b+3=0

a = 10; b = -810; c = +3;
Δ = b2-4ac
Δ = -8102-4·10·3
Δ = 655980
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:

$\sqrt{\Delta}=\sqrt{655980}=\sqrt{3364*195}=\sqrt{3364}*\sqrt{195}=58\sqrt{195}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-810)-58\sqrt{195}}{2*10}=\frac{810-58\sqrt{195}}{20}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-810)+58\sqrt{195}}{2*10}=\frac{810+58\sqrt{195}}{20}
$