1/2y=16+3y

Solution for 1/2y=16+3y equation:

1/2y=16+3y

We move all terms to the left:

1/2y-(16+3y)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

1/2y-(3y+16)=0

We get rid of parentheses

1/2y-3y-16=0

We multiply all the terms by the denominator


-3y*2y-16*2y+1=0

Wy multiply elements

-6y^2-32y+1=0

a = -6; b = -32; c = +1;
Δ = b2-4ac
Δ = -322-4·(-6)·1
Δ = 1048
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:

$\sqrt{\Delta}=\sqrt{1048}=\sqrt{4*262}=\sqrt{4}*\sqrt{262}=2\sqrt{262}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{262}}{2*-6}=\frac{32-2\sqrt{262}}{-12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{262}}{2*-6}=\frac{32+2\sqrt{262}}{-12}
$