20-1/5d=3/10d+14

Solution for 20-1/5d=3/10d+14 equation:

20-1/5d=3/10d+14

We move all terms to the left:

20-1/5d-(3/10d+14)=0


Domain of the equation: 5d!=0

d!=0/5

d!=0

d∈R



Domain of the equation: 10d+14)!=0

d∈R


We get rid of parentheses

-1/5d-3/10d-14+20=0

We calculate fractions


(-10d)/50d^2+(-15d)/50d^2-14+20=0

We add all the numbers together, and all the variables

(-10d)/50d^2+(-15d)/50d^2+6=0

We multiply all the terms by the denominator


(-10d)+(-15d)+6*50d^2=0

Wy multiply elements

300d^2+(-10d)+(-15d)=0

We get rid of parentheses

300d^2-10d-15d=0

We add all the numbers together, and all the variables

300d^2-25d=0

a = 300; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·300·0
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*300}=\frac{0}{600}
=0
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*300}=\frac{50}{600}
=1/12
$