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

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

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

We move all terms to the left:

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


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 5y+5)!=0

y∈R


We get rid of parentheses

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

We calculate fractions


(-75y^2)/540y^2+360y/540y^2+(-216y)/540y^2-5=0

We multiply all the terms by the denominator


(-75y^2)+360y+(-216y)-5*540y^2=0

Wy multiply elements

(-75y^2)-2700y^2+360y+(-216y)=0

We get rid of parentheses

-75y^2-2700y^2+360y-216y=0

We add all the numbers together, and all the variables

-2775y^2+144y=0

a = -2775; b = 144; c = 0;
Δ = b2-4ac
Δ = 1442-4·(-2775)·0
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-144}{2*-2775}=\frac{-288}{-5550}
=48/925
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+144}{2*-2775}=\frac{0}{-5550}
=0
$