23/5d-3/8d=47/10

Solution for 23/5d-3/8d=47/10 equation:

23/5d-3/8d=47/10

We move all terms to the left:

23/5d-3/8d-(47/10)=0


Domain of the equation: 5d!=0

d!=0/5

d!=0

d∈R



Domain of the equation: 8d!=0

d!=0/8

d!=0

d∈R


We add all the numbers together, and all the variables

23/5d-3/8d-(+47/10)=0

We get rid of parentheses

23/5d-3/8d-47/10=0

We calculate fractions


(-15040d^2)/400d^2+1840d/400d^2+(-150d)/400d^2=0

We multiply all the terms by the denominator


(-15040d^2)+1840d+(-150d)=0

We get rid of parentheses

-15040d^2+1840d-150d=0

We add all the numbers together, and all the variables

-15040d^2+1690d=0

a = -15040; b = 1690; c = 0;
Δ = b2-4ac
Δ = 16902-4·(-15040)·0
Δ = 2856100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2856100}=1690$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1690)-1690}{2*-15040}=\frac{-3380}{-30080}
=169/1504
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1690)+1690}{2*-15040}=\frac{0}{-30080}
=0
$