2d-6=1/4d+1

Solution for 2d-6=1/4d+1 equation:

2d-6=1/4d+1

We move all terms to the left:

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


Domain of the equation: 4d+1)!=0

d∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

8d^2-4d-24d-1=0

We add all the numbers together, and all the variables

8d^2-28d-1=0

a = 8; b = -28; c = -1;
Δ = b2-4ac
Δ = -282-4·8·(-1)
Δ = 816
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:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{51}}{2*8}=\frac{28-4\sqrt{51}}{16}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{51}}{2*8}=\frac{28+4\sqrt{51}}{16}
$