2-1/2y=3y+16

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

2-1/2y=3y+16

We move all terms to the left:

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


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-6y^2-32y+4y-1=0

We add all the numbers together, and all the variables

-6y^2-28y-1=0

a = -6; b = -28; c = -1;
Δ = b2-4ac
Δ = -282-4·(-6)·(-1)
Δ = 760
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:

$\sqrt{\Delta}=\sqrt{760}=\sqrt{4*190}=\sqrt{4}*\sqrt{190}=2\sqrt{190}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{190}}{2*-6}=\frac{28-2\sqrt{190}}{-12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{190}}{2*-6}=\frac{28+2\sqrt{190}}{-12}
$