(1)/(10)d-5=(3)/(5)d

Solution for (1)/(10)d-5=(3)/(5)d equation:

(1)/(10)d-5=(3)/(5)d

We move all terms to the left:

(1)/(10)d-5-((3)/(5)d)=0


Domain of the equation: 10d!=0

d!=0/10

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

1/10d-(+3/5d)-5=0

We get rid of parentheses

1/10d-3/5d-5=0

We calculate fractions


5d/50d^2+(-30d)/50d^2-5=0

We multiply all the terms by the denominator


5d+(-30d)-5*50d^2=0

Wy multiply elements

-250d^2+5d+(-30d)=0

We get rid of parentheses

-250d^2+5d-30d=0

We add all the numbers together, and all the variables

-250d^2-25d=0

a = -250; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·(-250)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*-250}=\frac{0}{-500}
=0
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*-250}=\frac{50}{-500}
=-1/10
$