3/2(y)-2/3=1/5(y)

Solution for 3/2(y)-2/3=1/5(y) equation:

3/2(y)-2/3=1/5(y)

We move all terms to the left:

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


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 5y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-100y^2)/90y^2+135y/90y^2+(-18y)/90y^2=0

We multiply all the terms by the denominator


(-100y^2)+135y+(-18y)=0

We get rid of parentheses

-100y^2+135y-18y=0

We add all the numbers together, and all the variables

-100y^2+117y=0

a = -100; b = 117; c = 0;
Δ = b2-4ac
Δ = 1172-4·(-100)·0
Δ = 13689
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13689}=117$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(117)-117}{2*-100}=\frac{-234}{-200}
=1+17/100
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(117)+117}{2*-100}=\frac{0}{-200}
=0
$