20-1/5d=1/3d+16

Solution for 20-1/5d=1/3d+16 equation:

20-1/5d=1/3d+16

We move all terms to the left:

20-1/5d-(1/3d+16)=0


Domain of the equation: 5d!=0

d!=0/5

d!=0

d∈R



Domain of the equation: 3d+16)!=0

d∈R


We get rid of parentheses

-1/5d-1/3d-16+20=0

We calculate fractions


(-3d)/15d^2+(-5d)/15d^2-16+20=0

We add all the numbers together, and all the variables

(-3d)/15d^2+(-5d)/15d^2+4=0

We multiply all the terms by the denominator


(-3d)+(-5d)+4*15d^2=0

Wy multiply elements

60d^2+(-3d)+(-5d)=0

We get rid of parentheses

60d^2-3d-5d=0

We add all the numbers together, and all the variables

60d^2-8d=0

a = 60; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·60·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*60}=\frac{0}{120}
=0
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*60}=\frac{16}{120}
=2/15
$