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

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

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

We move all terms to the left:

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


Domain of the equation: 2d!=0

d!=0/2

d!=0

d∈R



Domain of the equation: 5d)!=0

d!=0/1

d!=0

d∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-150d^2)/160d^2+80d/160d^2+(-96d)/160d^2=0

We multiply all the terms by the denominator


(-150d^2)+80d+(-96d)=0

We get rid of parentheses

-150d^2+80d-96d=0

We add all the numbers together, and all the variables

-150d^2-16d=0

a = -150; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-150)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*-150}=\frac{0}{-300}
=0
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-150}=\frac{32}{-300}
=-8/75
$