2/3y+3/2y=-15

Solution for 2/3y+3/2y=-15 equation:

2/3y+3/2y=-15

We move all terms to the left:

2/3y+3/2y-(-15)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

2/3y+3/2y+15=0

We calculate fractions


4y/6y^2+9y/6y^2+15=0

We multiply all the terms by the denominator


4y+9y+15*6y^2=0

We add all the numbers together, and all the variables

13y+15*6y^2=0

Wy multiply elements

90y^2+13y=0

a = 90; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·90·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*90}=\frac{-26}{180}
=-13/90
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*90}=\frac{0}{180}
=0
$