12/y+y=-7

Solution for 12/y+y=-7 equation:

12/y+y=-7

We move all terms to the left:

12/y+y-(-7)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

y+12/y+7=0

We multiply all the terms by the denominator


y*y+7*y+12=0

We add all the numbers together, and all the variables

7y+y*y+12=0

Wy multiply elements

y^2+7y+12=0

a = 1; b = 7; c = +12;
Δ = b2-4ac
Δ = 72-4·1·12
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-1}{2*1}=\frac{-8}{2}
=-4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+1}{2*1}=\frac{-6}{2}
=-3
$