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

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

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

We move all terms to the left:

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


Domain of the equation: 5d!=0

d!=0/5

d!=0

d∈R



Domain of the equation: 20d+16)!=0

d∈R


We get rid of parentheses

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

We calculate fractions


(-20d)/100d^2+(-15d)/100d^2-16+20=0

We add all the numbers together, and all the variables

(-20d)/100d^2+(-15d)/100d^2+4=0

We multiply all the terms by the denominator


(-20d)+(-15d)+4*100d^2=0

Wy multiply elements

400d^2+(-20d)+(-15d)=0

We get rid of parentheses

400d^2-20d-15d=0

We add all the numbers together, and all the variables

400d^2-35d=0

a = 400; b = -35; c = 0;
Δ = b2-4ac
Δ = -352-4·400·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-35}{2*400}=\frac{0}{800}
=0
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+35}{2*400}=\frac{70}{800}
=7/80
$