120-3/8d=200-4/5d

Solution for 120-3/8d=200-4/5d equation:

120-3/8d=200-4/5d

We move all terms to the left:

120-3/8d-(200-4/5d)=0


Domain of the equation: 8d!=0

d!=0/8

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

-3/8d-(-4/5d+200)+120=0

We get rid of parentheses

-3/8d+4/5d-200+120=0

We calculate fractions


(-15d)/40d^2+32d/40d^2-200+120=0

We add all the numbers together, and all the variables

(-15d)/40d^2+32d/40d^2-80=0

We multiply all the terms by the denominator


(-15d)+32d-80*40d^2=0

We add all the numbers together, and all the variables

32d+(-15d)-80*40d^2=0

Wy multiply elements

-3200d^2+32d+(-15d)=0

We get rid of parentheses

-3200d^2+32d-15d=0

We add all the numbers together, and all the variables

-3200d^2+17d=0

a = -3200; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-3200)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-3200}=\frac{-34}{-6400}
=17/3200
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-3200}=\frac{0}{-6400}
=0
$