2/3b+7=6b

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

2/3b+7=6b

We move all terms to the left:

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


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


-6b*3b+7*3b+2=0

Wy multiply elements

-18b^2+21b+2=0

a = -18; b = 21; c = +2;
Δ = b2-4ac
Δ = 212-4·(-18)·2
Δ = 585
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:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{65}}{2*-18}=\frac{-21-3\sqrt{65}}{-36}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{65}}{2*-18}=\frac{-21+3\sqrt{65}}{-36}
$