/6y+16-2y=-32

Solution for /6y+16-2y=-32 equation:

/6y+16-2y=-32

We move all terms to the left:

/6y+16-2y-(-32)=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R


We add all the numbers together, and all the variables

-2y+/6y+48=0

We multiply all the terms by the denominator


-2y*6y+48*6y+=0

We add all the numbers together, and all the variables

-2y*6y+48*6y=0

Wy multiply elements

-12y^2+288y=0

a = -12; b = 288; c = 0;
Δ = b2-4ac
Δ = 2882-4·(-12)·0
Δ = 82944
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{82944}=288$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(288)-288}{2*-12}=\frac{-576}{-24}
=+24
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(288)+288}{2*-12}=\frac{0}{-24}
=0
$