8k^2=6-4k

Solution for 8k^2=6-4k equation:

8k^2=6-4k

We move all terms to the left:

8k^2-(6-4k)=0

We add all the numbers together, and all the variables

8k^2-(-4k+6)=0

We get rid of parentheses

8k^2+4k-6=0

a = 8; b = 4; c = -6;
Δ = b2-4ac
Δ = 42-4·8·(-6)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{13}}{2*8}=\frac{-4-4\sqrt{13}}{16}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{13}}{2*8}=\frac{-4+4\sqrt{13}}{16}
$