3-1/2d=3/2d+-d

Solution for 3-1/2d=3/2d+-d equation:

3-1/2d=3/2d+-d

We move all terms to the left:

3-1/2d-(3/2d+-d)=0


Domain of the equation: 2d!=0

d!=0/2

d!=0

d∈R



Domain of the equation: 2d+-d)!=0

d∈R


We add all the numbers together, and all the variables

-1/2d-(-1d+3/2d)+3=0

We get rid of parentheses

-1/2d+1d-3/2d+3=0

We multiply all the terms by the denominator


1d*2d+3*2d-1-3=0

We add all the numbers together, and all the variables

1d*2d+3*2d-4=0

Wy multiply elements

2d^2+6d-4=0

a = 2; b = 6; c = -4;
Δ = b2-4ac
Δ = 62-4·2·(-4)
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{17}}{2*2}=\frac{-6-2\sqrt{17}}{4}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{17}}{2*2}=\frac{-6+2\sqrt{17}}{4}
$