2k^2-16k+18=0

Solution for 2k^2-16k+18=0 equation:

2k^2-16k+18=0

a = 2; b = -16; c = +18;
Δ = b2-4ac
Δ = -162-4·2·18
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{7}}{2*2}=\frac{16-4\sqrt{7}}{4}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{7}}{2*2}=\frac{16+4\sqrt{7}}{4}
$