2d(d-3)=1+4d

Solution for 2d(d-3)=1+4d equation:

2d(d-3)=1+4d

We move all terms to the left:

2d(d-3)-(1+4d)=0

We add all the numbers together, and all the variables

2d(d-3)-(4d+1)=0

We multiply parentheses

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

We get rid of parentheses

2d^2-6d-4d-1=0

We add all the numbers together, and all the variables

2d^2-10d-1=0

a = 2; b = -10; c = -1;
Δ = b2-4ac
Δ = -102-4·2·(-1)
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6\sqrt{3}}{2*2}=\frac{10-6\sqrt{3}}{4}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6\sqrt{3}}{2*2}=\frac{10+6\sqrt{3}}{4}
$