495=3b+3/2b

Solution for 495=3b+3/2b equation:

495=3b+3/2b

We move all terms to the left:

495-(3b+3/2b)=0


Domain of the equation: 2b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

-(+3b+3/2b)+495=0

We get rid of parentheses

-3b-3/2b+495=0

We multiply all the terms by the denominator


-3b*2b+495*2b-3=0

Wy multiply elements

-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}
$