5.5-1/3y-y=2

Solution for 5.5-1/3y-y=2 equation:

5.5-1/3y-y=2

We move all terms to the left:

5.5-1/3y-y-(2)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

-1y-1/3y+3.5=0

We multiply all the terms by the denominator


-1y*3y+(3.5)*3y-1=0

We multiply parentheses

-1y*3y+10.5y-1=0

Wy multiply elements

-3y^2+10.5y-1=0

a = -3; b = 10.5; c = -1;
Δ = b2-4ac
Δ = 10.52-4·(-3)·(-1)
Δ = 98.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10.5)-\sqrt{98.25}}{2*-3}=\frac{-10.5-\sqrt{98.25}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10.5)+\sqrt{98.25}}{2*-3}=\frac{-10.5+\sqrt{98.25}}{-6}
$