1/3d+10=3/5d

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

1/3d+10=3/5d

We move all terms to the left:

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


Domain of the equation: 3d!=0

d!=0/3

d!=0

d∈R



Domain of the equation: 5d)!=0

d!=0/1

d!=0

d∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


5d/15d^2+(-9d)/15d^2+10=0

We multiply all the terms by the denominator


5d+(-9d)+10*15d^2=0

Wy multiply elements

150d^2+5d+(-9d)=0

We get rid of parentheses

150d^2+5d-9d=0

We add all the numbers together, and all the variables

150d^2-4d=0

a = 150; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·150·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*150}=\frac{0}{300}
=0
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*150}=\frac{8}{300}
=2/75
$