-1/2d+2=-4d+2

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

-1/2d+2=-4d+2

We move all terms to the left:

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


Domain of the equation: 2d!=0

d!=0/2

d!=0

d∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

8d^2-1=0

a = 8; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·8·(-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{-(0)-4\sqrt{2}}{2*8}=\frac{0-4\sqrt{2}}{16}
=-\frac{4\sqrt{2}}{16}
=-\frac{\sqrt{2}}{4}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{2}}{2*8}=\frac{0+4\sqrt{2}}{16}
=\frac{4\sqrt{2}}{16}
=\frac{\sqrt{2}}{4}
$