4k^2-6=8k

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

4k^2-6=8k

We move all terms to the left:

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

a = 4; b = -8; c = -6;
Δ = b2-4ac
Δ = -82-4·4·(-6)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{10}}{2*4}=\frac{8-4\sqrt{10}}{8}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{10}}{2*4}=\frac{8+4\sqrt{10}}{8}
$