2*b-7=1/3*b+3

Solution for 2*b-7=1/3*b+3 equation:

2b-7=1/3b+3

We move all terms to the left:

2b-7-(1/3b+3)=0


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

b∈R


We get rid of parentheses

2b-1/3b-3-7=0

We multiply all the terms by the denominator


2b*3b-3*3b-7*3b-1=0

Wy multiply elements

6b^2-9b-21b-1=0

We add all the numbers together, and all the variables

6b^2-30b-1=0

a = 6; b = -30; c = -1;
Δ = b2-4ac
Δ = -302-4·6·(-1)
Δ = 924
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:

$\sqrt{\Delta}=\sqrt{924}=\sqrt{4*231}=\sqrt{4}*\sqrt{231}=2\sqrt{231}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{231}}{2*6}=\frac{30-2\sqrt{231}}{12}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{231}}{2*6}=\frac{30+2\sqrt{231}}{12}
$