2k2-k=1

Solution for 2k2-k=1 equation:

2k^2-k=1

We move all terms to the left:

2k^2-k-(1)=0

We add all the numbers together, and all the variables

2k^2-1k-1=0

a = 2; b = -1; c = -1;
Δ = b2-4ac
Δ = -12-4·2·(-1)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3}{2*2}=\frac{-2}{4}
=-1/2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3}{2*2}=\frac{4}{4}
=1
$