x+21/x=-10

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

x+21/x=-10

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+21/x+10=0

We multiply all the terms by the denominator


x*x+10*x+21=0

We add all the numbers together, and all the variables

10x+x*x+21=0

Wy multiply elements

x^2+10x+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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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