20k(k+2)=17K-6

Solution for 20k(k+2)=17K-6 equation:

20k(k+2)=17-6

We move all terms to the left:

20k(k+2)-(17-6)=0

We add all the numbers together, and all the variables

20k(k+2)-11=0

We multiply parentheses

20k^2+40k-11=0

a = 20; b = 40; c = -11;
Δ = b2-4ac
Δ = 402-4·20·(-11)
Δ = 2480
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:

$\sqrt{\Delta}=\sqrt{2480}=\sqrt{16*155}=\sqrt{16}*\sqrt{155}=4\sqrt{155}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{155}}{2*20}=\frac{-40-4\sqrt{155}}{40}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{155}}{2*20}=\frac{-40+4\sqrt{155}}{40}
$