1/2d-5=3/4d

Solution for 1/2d-5=3/4d equation:

1/2d-5=3/4d

We move all terms to the left:

1/2d-5-(3/4d)=0


Domain of the equation: 2d!=0

d!=0/2

d!=0

d∈R



Domain of the equation: 4d)!=0

d!=0/1

d!=0

d∈R


We add all the numbers together, and all the variables

1/2d-(+3/4d)-5=0

We get rid of parentheses

1/2d-3/4d-5=0

We calculate fractions


4d/8d^2+(-6d)/8d^2-5=0

We multiply all the terms by the denominator


4d+(-6d)-5*8d^2=0

Wy multiply elements

-40d^2+4d+(-6d)=0

We get rid of parentheses

-40d^2+4d-6d=0

We add all the numbers together, and all the variables

-40d^2-2d=0

a = -40; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-40)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-40}=\frac{0}{-80}
=0
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-40}=\frac{4}{-80}
=-1/20
$