1/2d+6=d+8

Solution for 1/2d+6=d+8 equation:

1/2d+6=d+8

We move all terms to the left:

1/2d+6-(d+8)=0


Domain of the equation: 2d!=0

d!=0/2

d!=0

d∈R


We get rid of parentheses

1/2d-d-8+6=0

We multiply all the terms by the denominator


-d*2d-8*2d+6*2d+1=0

Wy multiply elements

-2d^2-16d+12d+1=0

We add all the numbers together, and all the variables

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

a = -2; b = -4; c = +1;
Δ = b2-4ac
Δ = -42-4·(-2)·1
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{6}}{2*-2}=\frac{4-2\sqrt{6}}{-4}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{6}}{2*-2}=\frac{4+2\sqrt{6}}{-4}
$