5k^2-11=-2k

Solution for 5k^2-11=-2k equation:

5k^2-11=-2k

We move all terms to the left:

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

We get rid of parentheses

5k^2+2k-11=0

a = 5; b = 2; c = -11;
Δ = b2-4ac
Δ = 22-4·5·(-11)
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{14}}{2*5}=\frac{-2-4\sqrt{14}}{10}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{14}}{2*5}=\frac{-2+4\sqrt{14}}{10}
$