k^2-k-(7/4)=0

Solution for k^2-k-(7/4)=0 equation:

k^2-k-(7/4)=0

We add all the numbers together, and all the variables

k^2-k-(+7/4)=0

We add all the numbers together, and all the variables

k^2-1k-(+7/4)=0

We get rid of parentheses

k^2-1k-7/4=0

We multiply all the terms by the denominator


k^2*4-1k*4-7=0

Wy multiply elements

4k^2-4k-7=0

a = 4; b = -4; c = -7;
Δ = b2-4ac
Δ = -42-4·4·(-7)
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8\sqrt{2}}{2*4}=\frac{4-8\sqrt{2}}{8}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8\sqrt{2}}{2*4}=\frac{4+8\sqrt{2}}{8}
$