2/5y+4=5/6y+2

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

2/5y+4=5/6y+2

We move all terms to the left:

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


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 6y+2)!=0

y∈R


We get rid of parentheses

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

We calculate fractions


12y/30y^2+(-25y)/30y^2-2+4=0

We add all the numbers together, and all the variables

12y/30y^2+(-25y)/30y^2+2=0

We multiply all the terms by the denominator


12y+(-25y)+2*30y^2=0

Wy multiply elements

60y^2+12y+(-25y)=0

We get rid of parentheses

60y^2+12y-25y=0

We add all the numbers together, and all the variables

60y^2-13y=0

a = 60; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·60·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*60}=\frac{0}{120}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*60}=\frac{26}{120}
=13/60
$