20-1/5d=3/10d=3/10d+16

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Solution for 20-1/5d=3/10d=3/10d+16 equation:



20-1/5d=3/10d=3/10d+16
We move all terms to the left:
20-1/5d-(3/10d)=0
Domain of the equation: 5d!=0
d!=0/5
d!=0
d∈R
Domain of the equation: 10d)!=0
d!=0/1
d!=0
d∈R
We add all the numbers together, and all the variables
-1/5d-(+3/10d)+20=0
We get rid of parentheses
-1/5d-3/10d+20=0
We calculate fractions
(-10d)/50d^2+(-15d)/50d^2+20=0
We multiply all the terms by the denominator
(-10d)+(-15d)+20*50d^2=0
Wy multiply elements
1000d^2+(-10d)+(-15d)=0
We get rid of parentheses
1000d^2-10d-15d=0
We add all the numbers together, and all the variables
1000d^2-25d=0
a = 1000; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·1000·0
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*1000}=\frac{0}{2000} =0 $
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*1000}=\frac{50}{2000} =1/40 $

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