4k^2=-k+1

Solution for 4k^2=-k+1 equation:

4k^2=-k+1

We move all terms to the left:

4k^2-(-k+1)=0

We add all the numbers together, and all the variables

4k^2-(-1k+1)=0

We get rid of parentheses

4k^2+1k-1=0

We add all the numbers together, and all the variables

4k^2+k-1=0

a = 4; b = 1; c = -1;
Δ = b2-4ac
Δ = 12-4·4·(-1)
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{17}}{2*4}=\frac{-1-\sqrt{17}}{8}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{17}}{2*4}=\frac{-1+\sqrt{17}}{8}
$