5d^2+6d+1=4d^2

Solution for 5d^2+6d+1=4d^2 equation:

5d^2+6d+1=4d^2

We move all terms to the left:

5d^2+6d+1-(4d^2)=0

determiningTheFunctionDomain
5d^2-4d^2+6d+1=0

We add all the numbers together, and all the variables

d^2+6d+1=0

a = 1; b = 6; c = +1;
Δ = b2-4ac
Δ = 62-4·1·1
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{-(6)-4\sqrt{2}}{2*1}=\frac{-6-4\sqrt{2}}{2}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{2}}{2*1}=\frac{-6+4\sqrt{2}}{2}
$