1/2d-11=d

Solution for 1/2d-11=d equation:

1/2d-11=d

We move all terms to the left:

1/2d-11-(d)=0


Domain of the equation: 2d!=0

d!=0/2

d!=0

d∈R


We add all the numbers together, and all the variables

-1d+1/2d-11=0

We multiply all the terms by the denominator


-1d*2d-11*2d+1=0

Wy multiply elements

-2d^2-22d+1=0

a = -2; b = -22; c = +1;
Δ = b2-4ac
Δ = -222-4·(-2)·1
Δ = 492
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:

$\sqrt{\Delta}=\sqrt{492}=\sqrt{4*123}=\sqrt{4}*\sqrt{123}=2\sqrt{123}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{123}}{2*-2}=\frac{22-2\sqrt{123}}{-4}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{123}}{2*-2}=\frac{22+2\sqrt{123}}{-4}
$