1/2b-9+3b=19

Solution for 1/2b-9+3b=19 equation:

1/2b-9+3b=19

We move all terms to the left:

1/2b-9+3b-(19)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We add all the numbers together, and all the variables

3b+1/2b-28=0

We multiply all the terms by the denominator


3b*2b-28*2b+1=0

Wy multiply elements

6b^2-56b+1=0

a = 6; b = -56; c = +1;
Δ = b2-4ac
Δ = -562-4·6·1
Δ = 3112
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:

$\sqrt{\Delta}=\sqrt{3112}=\sqrt{4*778}=\sqrt{4}*\sqrt{778}=2\sqrt{778}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-2\sqrt{778}}{2*6}=\frac{56-2\sqrt{778}}{12}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+2\sqrt{778}}{2*6}=\frac{56+2\sqrt{778}}{12}
$