20-1/5d=7/10d+16

Solution for 20-1/5d=7/10d+16 equation:

20-1/5d=7/10d+16

We move all terms to the left:

20-1/5d-(7/10d+16)=0


Domain of the equation: 5d!=0

d!=0/5

d!=0

d∈R



Domain of the equation: 10d+16)!=0

d∈R


We get rid of parentheses

-1/5d-7/10d-16+20=0

We calculate fractions


(-10d)/50d^2+(-35d)/50d^2-16+20=0

We add all the numbers together, and all the variables

(-10d)/50d^2+(-35d)/50d^2+4=0

We multiply all the terms by the denominator


(-10d)+(-35d)+4*50d^2=0

Wy multiply elements

200d^2+(-10d)+(-35d)=0

We get rid of parentheses

200d^2-10d-35d=0

We add all the numbers together, and all the variables

200d^2-45d=0

a = 200; b = -45; c = 0;
Δ = b2-4ac
Δ = -452-4·200·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-45}{2*200}=\frac{0}{400}
=0
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+45}{2*200}=\frac{90}{400}
=9/40
$