4d+1=4d^2

Solution for 4d+1=4d^2 equation:

4d+1=4d^2

We move all terms to the left:

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

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

a = -4; b = 4; c = +1;
Δ = b2-4ac
Δ = 42-4·(-4)·1
Δ = 32
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{2}}{2*-4}=\frac{-4-4\sqrt{2}}{-8}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{2}}{2*-4}=\frac{-4+4\sqrt{2}}{-8}
$