d^2+d+1/4-1=0

Solution for d^2+d+1/4-1=0 equation:

d^2+d+1/4-1=0

We multiply all the terms by the denominator


d^2*4+d*4+1-1*4=0

We add all the numbers together, and all the variables

d^2*4+d*4-3=0

Wy multiply elements

4d^2+4d-3=0

a = 4; b = 4; c = -3;
Δ = b2-4ac
Δ = 42-4·4·(-3)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8}{2*4}=\frac{-12}{8}
=-1+1/2
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8}{2*4}=\frac{4}{8}
=1/2
$