3/5y+12=-1/3y+7

Solution for 3/5y+12=-1/3y+7 equation:

3/5y+12=-1/3y+7

We move all terms to the left:

3/5y+12-(-1/3y+7)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 3y+7)!=0

y∈R


We get rid of parentheses

3/5y+1/3y-7+12=0

We calculate fractions


9y/15y^2+5y/15y^2-7+12=0

We add all the numbers together, and all the variables

9y/15y^2+5y/15y^2+5=0

We multiply all the terms by the denominator


9y+5y+5*15y^2=0

We add all the numbers together, and all the variables

14y+5*15y^2=0

Wy multiply elements

75y^2+14y=0

a = 75; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·75·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*75}=\frac{-28}{150}
=-14/75
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*75}=\frac{0}{150}
=0
$