3/5y-(y+9)=-12

Solution for 3/5y-(y+9)=-12 equation:

3/5y-(y+9)=-12

We move all terms to the left:

3/5y-(y+9)-(-12)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

3/5y-(y+9)+12=0

We get rid of parentheses

3/5y-y-9+12=0

We multiply all the terms by the denominator


-y*5y-9*5y+12*5y+3=0

Wy multiply elements

-5y^2-45y+60y+3=0

We add all the numbers together, and all the variables

-5y^2+15y+3=0

a = -5; b = 15; c = +3;
Δ = b2-4ac
Δ = 152-4·(-5)·3
Δ = 285
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{285}}{2*-5}=\frac{-15-\sqrt{285}}{-10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{285}}{2*-5}=\frac{-15+\sqrt{285}}{-10}
$