0.25+k+k^2=1

Solution for 0.25+k+k^2=1 equation:

0.25+k+k^2=1

We move all terms to the left:

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

We add all the numbers together, and all the variables

k^2+k-0.75=0

a = 1; b = 1; c = -0.75;
Δ = b2-4ac
Δ = 12-4·1·(-0.75)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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