-k=9k(k-10)

Solution for -k=9k(k-10) equation:

-k=9k(k-10)

We move all terms to the left:

-k-(9k(k-10))=0

We add all the numbers together, and all the variables

-1k-(9k(k-10))=0


We calculate terms in parentheses: -(9k(k-10)), so:

9k(k-10)

We multiply parentheses

9k^2-90k

Back to the equation:

-(9k^2-90k)


We get rid of parentheses

-9k^2-1k+90k=0

We add all the numbers together, and all the variables

-9k^2+89k=0

a = -9; b = 89; c = 0;
Δ = b2-4ac
Δ = 892-4·(-9)·0
Δ = 7921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7921}=89$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(89)-89}{2*-9}=\frac{-178}{-18}
=9+8/9
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(89)+89}{2*-9}=\frac{0}{-18}
=0
$