1/2y-9+3y=19

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

1/2y-9+3y=19

We move all terms to the left:

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


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

3y+1/2y-28=0

We multiply all the terms by the denominator


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

Wy multiply elements

6y^2-56y+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:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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