11b+1=2/3b+8

Solution for 11b+1=2/3b+8 equation:

11b+1=2/3b+8

We move all terms to the left:

11b+1-(2/3b+8)=0


Domain of the equation: 3b+8)!=0

b∈R


We get rid of parentheses

11b-2/3b-8+1=0

We multiply all the terms by the denominator


11b*3b-8*3b+1*3b-2=0

Wy multiply elements

33b^2-24b+3b-2=0

We add all the numbers together, and all the variables

33b^2-21b-2=0

a = 33; b = -21; c = -2;
Δ = b2-4ac
Δ = -212-4·33·(-2)
Δ = 705
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{705}}{2*33}=\frac{21-\sqrt{705}}{66}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{705}}{2*33}=\frac{21+\sqrt{705}}{66}
$