-k(k+9)=9(k-5)-14

Solution for -k(k+9)=9(k-5)-14 equation:

-k(k+9)=9(k-5)-14

We move all terms to the left:

-k(k+9)-(9(k-5)-14)=0

We multiply parentheses

-k^2-9k-(9(k-5)-14)=0


We calculate terms in parentheses: -(9(k-5)-14), so:

9(k-5)-14

We multiply parentheses

9k-45-14

We add all the numbers together, and all the variables

9k-59

Back to the equation:

-(9k-59)


We add all the numbers together, and all the variables

-1k^2-9k-(9k-59)=0

We get rid of parentheses

-1k^2-9k-9k+59=0

We add all the numbers together, and all the variables

-1k^2-18k+59=0

a = -1; b = -18; c = +59;
Δ = b2-4ac
Δ = -182-4·(-1)·59
Δ = 560
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:

$\sqrt{\Delta}=\sqrt{560}=\sqrt{16*35}=\sqrt{16}*\sqrt{35}=4\sqrt{35}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-4\sqrt{35}}{2*-1}=\frac{18-4\sqrt{35}}{-2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+4\sqrt{35}}{2*-1}=\frac{18+4\sqrt{35}}{-2}
$