1/2b+7=b+14

Solution for 1/2b+7=b+14 equation:

1/2b+7=b+14

We move all terms to the left:

1/2b+7-(b+14)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We get rid of parentheses

1/2b-b-14+7=0

We multiply all the terms by the denominator


-b*2b-14*2b+7*2b+1=0

Wy multiply elements

-2b^2-28b+14b+1=0

We add all the numbers together, and all the variables

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

a = -2; b = -14; c = +1;
Δ = b2-4ac
Δ = -142-4·(-2)·1
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{51}}{2*-2}=\frac{14-2\sqrt{51}}{-4}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{51}}{2*-2}=\frac{14+2\sqrt{51}}{-4}
$