23-1/5d=3/10d+16

Solution for 23-1/5d=3/10d+16 equation:

23-1/5d=3/10d+16

We move all terms to the left:

23-1/5d-(3/10d+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-3/10d-16+23=0

We calculate fractions


(-10d)/50d^2+(-15d)/50d^2-16+23=0

We add all the numbers together, and all the variables

(-10d)/50d^2+(-15d)/50d^2+7=0

We multiply all the terms by the denominator


(-10d)+(-15d)+7*50d^2=0

Wy multiply elements

350d^2+(-10d)+(-15d)=0

We get rid of parentheses

350d^2-10d-15d=0

We add all the numbers together, and all the variables

350d^2-25d=0

a = 350; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·350·0
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*350}=\frac{0}{700}
=0
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*350}=\frac{50}{700}
=1/14
$