-10=y+21/y

Solution for -10=y+21/y equation:

-10=y+21/y

We move all terms to the left:

-10-(y+21/y)=0


Domain of the equation: y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

-(+y+21/y)-10=0

We get rid of parentheses

-y-21/y-10=0

We multiply all the terms by the denominator


-y*y-10*y-21=0

We add all the numbers together, and all the variables

-10y-y*y-21=0

Wy multiply elements

-1y^2-10y-21=0

a = -1; b = -10; c = -21;
Δ = b2-4ac
Δ = -102-4·(-1)·(-21)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4}{2*-1}=\frac{6}{-2}
=-3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4}{2*-1}=\frac{14}{-2}
=-7
$