1/8d-4+3/8d-4=d

Solution for 1/8d-4+3/8d-4=d equation:

1/8d-4+3/8d-4=d

We move all terms to the left:

1/8d-4+3/8d-4-(d)=0


Domain of the equation: 8d!=0

d!=0/8

d!=0

d∈R


We add all the numbers together, and all the variables

-1d+1/8d+3/8d-8=0

We multiply all the terms by the denominator


-1d*8d-8*8d+1+3=0

We add all the numbers together, and all the variables

-1d*8d-8*8d+4=0

Wy multiply elements

-8d^2-64d+4=0

a = -8; b = -64; c = +4;
Δ = b2-4ac
Δ = -642-4·(-8)·4
Δ = 4224
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:

$\sqrt{\Delta}=\sqrt{4224}=\sqrt{64*66}=\sqrt{64}*\sqrt{66}=8\sqrt{66}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-8\sqrt{66}}{2*-8}=\frac{64-8\sqrt{66}}{-16}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+8\sqrt{66}}{2*-8}=\frac{64+8\sqrt{66}}{-16}
$