1/2b+2/3b+7=21

Solution for 1/2b+2/3b+7=21 equation:

1/2b+2/3b+7=21

We move all terms to the left:

1/2b+2/3b+7-(21)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R



Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R


We add all the numbers together, and all the variables

1/2b+2/3b-14=0

We calculate fractions


3b/6b^2+4b/6b^2-14=0

We multiply all the terms by the denominator


3b+4b-14*6b^2=0

We add all the numbers together, and all the variables

7b-14*6b^2=0

Wy multiply elements

-84b^2+7b=0

a = -84; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-84)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-84}=\frac{-14}{-168}
=1/12
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-84}=\frac{0}{-168}
=0
$