1/2y-31/30=2/5y-1

Solution for 1/2y-31/30=2/5y-1 equation:

1/2y-31/30=2/5y-1

We move all terms to the left:

1/2y-31/30-(2/5y-1)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 5y-1)!=0

y∈R


We get rid of parentheses

1/2y-2/5y+1-31/30=0

We calculate fractions


(-1550y^2)/900y^2+450y/900y^2+(-360y)/900y^2+1=0

We multiply all the terms by the denominator


(-1550y^2)+450y+(-360y)+1*900y^2=0

Wy multiply elements

(-1550y^2)+900y^2+450y+(-360y)=0

We get rid of parentheses

-1550y^2+900y^2+450y-360y=0

We add all the numbers together, and all the variables

-650y^2+90y=0

a = -650; b = 90; c = 0;
Δ = b2-4ac
Δ = 902-4·(-650)·0
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-90}{2*-650}=\frac{-180}{-1300}
=9/65
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+90}{2*-650}=\frac{0}{-1300}
=0
$