11/6b+7/2b=8/3

Solution for 11/6b+7/2b=8/3 equation:

11/6b+7/2b=8/3

We move all terms to the left:

11/6b+7/2b-(8/3)=0


Domain of the equation: 6b!=0

b!=0/6

b!=0

b∈R



Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We add all the numbers together, and all the variables

11/6b+7/2b-(+8/3)=0

We get rid of parentheses

11/6b+7/2b-8/3=0

We calculate fractions


(-192b^2)/108b^2+198b/108b^2+378b/108b^2=0

We multiply all the terms by the denominator


(-192b^2)+198b+378b=0

We add all the numbers together, and all the variables

(-192b^2)+576b=0

We get rid of parentheses

-192b^2+576b=0

a = -192; b = 576; c = 0;
Δ = b2-4ac
Δ = 5762-4·(-192)·0
Δ = 331776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{331776}=576$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(576)-576}{2*-192}=\frac{-1152}{-384}
=+3
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(576)+576}{2*-192}=\frac{0}{-384}
=0
$