24k^2-40k+22=6

Solution for 24k^2-40k+22=6 equation:

24k^2-40k+22=6

We move all terms to the left:

24k^2-40k+22-(6)=0

We add all the numbers together, and all the variables

24k^2-40k+16=0

a = 24; b = -40; c = +16;
Δ = b2-4ac
Δ = -402-4·24·16
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8}{2*24}=\frac{32}{48}
=2/3
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8}{2*24}=\frac{48}{48}
=1
$