8k^2=2k+5

Solution for 8k^2=2k+5 equation:

8k^2=2k+5

We move all terms to the left:

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

We get rid of parentheses

8k^2-2k-5=0

a = 8; b = -2; c = -5;
Δ = b2-4ac
Δ = -22-4·8·(-5)
Δ = 164
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:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{41}}{2*8}=\frac{2-2\sqrt{41}}{16}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{41}}{2*8}=\frac{2+2\sqrt{41}}{16}
$