-9y+15=-4/y

Solution for -9y+15=-4/y equation:

-9y+15=-4/y

We move all terms to the left:

-9y+15-(-4/y)=0


Domain of the equation: y)!=0

y!=0/1

y!=0

y∈R


We get rid of parentheses

-9y+4/y+15=0

We multiply all the terms by the denominator


-9y*y+15*y+4=0

We add all the numbers together, and all the variables

15y-9y*y+4=0

Wy multiply elements

-9y^2+15y+4=0

a = -9; b = 15; c = +4;
Δ = b2-4ac
Δ = 152-4·(-9)·4
Δ = 369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{41}}{2*-9}=\frac{-15-3\sqrt{41}}{-18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{41}}{2*-9}=\frac{-15+3\sqrt{41}}{-18}
$