3k2=8k+8

Solution for 3k2=8k+8 equation:

3k^2=8k+8

We move all terms to the left:

3k^2-(8k+8)=0

We get rid of parentheses

3k^2-8k-8=0

a = 3; b = -8; c = -8;
Δ = b2-4ac
Δ = -82-4·3·(-8)
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*3}=\frac{8-4\sqrt{10}}{6}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{10}}{2*3}=\frac{8+4\sqrt{10}}{6}
$