-1/10k=k+1

Solution for -1/10k=k+1 equation:

-1/10k=k+1

We move all terms to the left:

-1/10k-(k+1)=0


Domain of the equation: 10k!=0

k!=0/10

k!=0

k∈R


We get rid of parentheses

-1/10k-k-1=0

We multiply all the terms by the denominator


-k*10k-1*10k-1=0

Wy multiply elements

-10k^2-10k-1=0

a = -10; b = -10; c = -1;
Δ = b2-4ac
Δ = -102-4·(-10)·(-1)
Δ = 60
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{15}}{2*-10}=\frac{10-2\sqrt{15}}{-20}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{15}}{2*-10}=\frac{10+2\sqrt{15}}{-20}
$