-1/2d+2=-4d-8

Solution for -1/2d+2=-4d-8 equation:

-1/2d+2=-4d-8

We move all terms to the left:

-1/2d+2-(-4d-8)=0


Domain of the equation: 2d!=0

d!=0/2

d!=0

d∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

8d^2+16d+4d-1=0

We add all the numbers together, and all the variables

8d^2+20d-1=0

a = 8; b = 20; c = -1;
Δ = b2-4ac
Δ = 202-4·8·(-1)
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-12\sqrt{3}}{2*8}=\frac{-20-12\sqrt{3}}{16}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+12\sqrt{3}}{2*8}=\frac{-20+12\sqrt{3}}{16}
$