5k^2+19k+11=2k

Solution for 5k^2+19k+11=2k equation:

5k^2+19k+11=2k

We move all terms to the left:

5k^2+19k+11-(2k)=0

We add all the numbers together, and all the variables

5k^2+17k+11=0

a = 5; b = 17; c = +11;
Δ = b2-4ac
Δ = 172-4·5·11
Δ = 69
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-\sqrt{69}}{2*5}=\frac{-17-\sqrt{69}}{10}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{69}}{2*5}=\frac{-17+\sqrt{69}}{10}
$