-3/2y-3/2=2/5y-2

Solution for -3/2y-3/2=2/5y-2 equation:

-3/2y-3/2=2/5y-2

We move all terms to the left:

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


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 5y-2)!=0

y∈R


We get rid of parentheses

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

We calculate fractions


(-15y)/40y^2+(-16y)/40y^2+(-15y)/40y^2+2=0

We multiply all the terms by the denominator


(-15y)+(-16y)+(-15y)+2*40y^2=0

Wy multiply elements

80y^2+(-15y)+(-16y)+(-15y)=0

We get rid of parentheses

80y^2-15y-16y-15y=0

We add all the numbers together, and all the variables

80y^2-46y=0

a = 80; b = -46; c = 0;
Δ = b2-4ac
Δ = -462-4·80·0
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-46}{2*80}=\frac{0}{160}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+46}{2*80}=\frac{92}{160}
=23/40
$