1/2b-17+5b+7=12

Solution for 1/2b-17+5b+7=12 equation:

1/2b-17+5b+7=12

We move all terms to the left:

1/2b-17+5b+7-(12)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We add all the numbers together, and all the variables

5b+1/2b-22=0

We multiply all the terms by the denominator


5b*2b-22*2b+1=0

Wy multiply elements

10b^2-44b+1=0

a = 10; b = -44; c = +1;
Δ = b2-4ac
Δ = -442-4·10·1
Δ = 1896
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:

$\sqrt{\Delta}=\sqrt{1896}=\sqrt{4*474}=\sqrt{4}*\sqrt{474}=2\sqrt{474}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-2\sqrt{474}}{2*10}=\frac{44-2\sqrt{474}}{20}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+2\sqrt{474}}{2*10}=\frac{44+2\sqrt{474}}{20}
$