1/2y-5/6y+1/3=1/2

Solution for 1/2y-5/6y+1/3=1/2 equation:

1/2y-5/6y+1/3=1/2

We move all terms to the left:

1/2y-5/6y+1/3-(1/2)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R


We add all the numbers together, and all the variables

1/2y-5/6y+1/3-(+1/2)=0

We get rid of parentheses

1/2y-5/6y+1/3-1/2=0

We calculate fractions


144y^2/216y^2+54y/216y^2+(-180y)/216y^2+(-54y)/216y^2=0

We multiply all the terms by the denominator


144y^2+54y+(-180y)+(-54y)=0

We get rid of parentheses

144y^2+54y-180y-54y=0

We add all the numbers together, and all the variables

144y^2-180y=0

a = 144; b = -180; c = 0;
Δ = b2-4ac
Δ = -1802-4·144·0
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-180}{2*144}=\frac{0}{288}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+180}{2*144}=\frac{360}{288}
=1+1/4
$