1/2y+5/6=4/3y-5

Solution for 1/2y+5/6=4/3y-5 equation:

1/2y+5/6=4/3y-5

We move all terms to the left:

1/2y+5/6-(4/3y-5)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 3y-5)!=0

y∈R


We get rid of parentheses

1/2y-4/3y+5+5/6=0

We calculate fractions


90y^2/216y^2+108y/216y^2+(-288y)/216y^2+5=0

We multiply all the terms by the denominator


90y^2+108y+(-288y)+5*216y^2=0

Wy multiply elements

90y^2+1080y^2+108y+(-288y)=0

We get rid of parentheses

90y^2+1080y^2+108y-288y=0

We add all the numbers together, and all the variables

1170y^2-180y=0

a = 1170; b = -180; c = 0;
Δ = b2-4ac
Δ = -1802-4·1170·0
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*1170}=\frac{0}{2340}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+180}{2*1170}=\frac{360}{2340}
=2/13
$