8k2=11+5k

Solution for 8k2=11+5k equation:

8k^2=11+5k

We move all terms to the left:

8k^2-(11+5k)=0

We add all the numbers together, and all the variables

8k^2-(5k+11)=0

We get rid of parentheses

8k^2-5k-11=0

a = 8; b = -5; c = -11;
Δ = b2-4ac
Δ = -52-4·8·(-11)
Δ = 377
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{-(-5)-\sqrt{377}}{2*8}=\frac{5-\sqrt{377}}{16}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{377}}{2*8}=\frac{5+\sqrt{377}}{16}
$