(5/3-b)*b=1/11

Solution for (5/3-b)*b=1/11 equation:

(5/3-b)*b=1/11

We move all terms to the left:

(5/3-b)*b-(1/11)=0


Domain of the equation: 3-b)*b!=0

We move all terms containing b to the left, all other terms to the right

-b)*b!=-3

b!=-3/1

b!=-3

b∈R


We add all the numbers together, and all the variables

(-1b+5/3)*b-(+1/11)=0

We multiply parentheses

-1b^2+5b^2-(+1/11)=0

We get rid of parentheses

-1b^2+5b^2-1/11=0

We multiply all the terms by the denominator


-1b^2*11+5b^2*11-1=0

Wy multiply elements

-11b^2+55b^2-1=0

We add all the numbers together, and all the variables

44b^2-1=0

a = 44; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·44·(-1)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{11}}{2*44}=\frac{0-4\sqrt{11}}{88}
=-\frac{4\sqrt{11}}{88}
=-\frac{\sqrt{11}}{22}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{11}}{2*44}=\frac{0+4\sqrt{11}}{88}
=\frac{4\sqrt{11}}{88}
=\frac{\sqrt{11}}{22}
$