1/(b+14)=b+14/2

Solution for 1/(b+14)=b+14/2 equation:

1/(b+14)=b+14/2

We move all terms to the left:

1/(b+14)-(b+14/2)=0


Domain of the equation: (b+14)!=0

We move all terms containing b to the left, all other terms to the right

b!=-14

b∈R


We add all the numbers together, and all the variables

1/(b+14)-(b+7)=0

We get rid of parentheses

1/(b+14)-b-7=0

We multiply all the terms by the denominator


-b*(b+14)-7*(b+14)+1=0

We multiply parentheses

-b^2-14b-7b-98+1=0

We add all the numbers together, and all the variables

-1b^2-21b-97=0

a = -1; b = -21; c = -97;
Δ = b2-4ac
Δ = -212-4·(-1)·(-97)
Δ = 53
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{53}}{2*-1}=\frac{21-\sqrt{53}}{-2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{53}}{2*-1}=\frac{21+\sqrt{53}}{-2}
$