3*2/5y-4=2-1/2y

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

3*2/5y-4=2-1/2y

We move all terms to the left:

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


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 2y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


24y/10y^2+5y/10y^2-2-4=0

We add all the numbers together, and all the variables

24y/10y^2+5y/10y^2-6=0

We multiply all the terms by the denominator


24y+5y-6*10y^2=0

We add all the numbers together, and all the variables

29y-6*10y^2=0

Wy multiply elements

-60y^2+29y=0

a = -60; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·(-60)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-29}{2*-60}=\frac{-58}{-120}
=29/60
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*-60}=\frac{0}{-120}
=0
$