b-0.12=1/3b+0.88

Solution for b-0.12=1/3b+0.88 equation:

b-0.12=1/3b+0.88

We move all terms to the left:

b-0.12-(1/3b+0.88)=0


Domain of the equation: 3b+0.88)!=0

b∈R


We get rid of parentheses

b-1/3b-0.88-0.12=0

We multiply all the terms by the denominator


b*3b-(0.88)*3b-(0.12)*3b-1=0

We multiply parentheses

b*3b-2.64b-0.36b-1=0

Wy multiply elements

3b^2-2.64b-0.36b-1=0

We add all the numbers together, and all the variables

3b^2-3b-1=0

a = 3; b = -3; c = -1;
Δ = b2-4ac
Δ = -32-4·3·(-1)
Δ = 21
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{-(-3)-\sqrt{21}}{2*3}=\frac{3-\sqrt{21}}{6}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{21}}{2*3}=\frac{3+\sqrt{21}}{6}
$