k+k^2=11/4

Solution for k+k^2=11/4 equation:

k+k^2=11/4

We move all terms to the left:

k+k^2-(11/4)=0

We add all the numbers together, and all the variables

k^2+k-(+11/4)=0

We get rid of parentheses

k^2+k-11/4=0

We multiply all the terms by the denominator


k^2*4+k*4-11=0

Wy multiply elements

4k^2+4k-11=0

a = 4; b = 4; c = -11;
Δ = b2-4ac
Δ = 42-4·4·(-11)
Δ = 192
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8\sqrt{3}}{2*4}=\frac{-4-8\sqrt{3}}{8}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8\sqrt{3}}{2*4}=\frac{-4+8\sqrt{3}}{8}
$