2k^2-12k-32=0

Solution for 2k^2-12k-32=0 equation:

2k^2-12k-32=0

a = 2; b = -12; c = -32;
Δ = b2-4ac
Δ = -122-4·2·(-32)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-20}{2*2}=\frac{-8}{4}
=-2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+20}{2*2}=\frac{32}{4}
=8
$