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

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

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

We move all terms to the left:

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


Domain of the equation: 5d!=0

d!=0/5

d!=0

d∈R



Domain of the equation: 3d-3)!=0

d∈R


We get rid of parentheses

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

We calculate fractions


9d/15d^2+(-5d)/15d^2+3+5=0

We add all the numbers together, and all the variables

9d/15d^2+(-5d)/15d^2+8=0

We multiply all the terms by the denominator


9d+(-5d)+8*15d^2=0

Wy multiply elements

120d^2+9d+(-5d)=0

We get rid of parentheses

120d^2+9d-5d=0

We add all the numbers together, and all the variables

120d^2+4d=0

a = 120; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·120·0
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*120}=\frac{-8}{240}
=-1/30
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*120}=\frac{0}{240}
=0
$