8k2-16k=42

Solution for 8k2-16k=42 equation:

8k^2-16k=42

We move all terms to the left:

8k^2-16k-(42)=0

a = 8; b = -16; c = -42;
Δ = b2-4ac
Δ = -162-4·8·(-42)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-40}{2*8}=\frac{-24}{16}
=-1+1/2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+40}{2*8}=\frac{56}{16}
=3+1/2
$