2/3d-3/5d=4

Solution for 2/3d-3/5d=4 equation:

2/3d-3/5d=4

We move all terms to the left:

2/3d-3/5d-(4)=0


Domain of the equation: 3d!=0

d!=0/3

d!=0

d∈R



Domain of the equation: 5d!=0

d!=0/5

d!=0

d∈R


We calculate fractions


10d/15d^2+(-9d)/15d^2-4=0

We multiply all the terms by the denominator


10d+(-9d)-4*15d^2=0

Wy multiply elements

-60d^2+10d+(-9d)=0

We get rid of parentheses

-60d^2+10d-9d=0

We add all the numbers together, and all the variables

-60d^2+d=0

a = -60; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-60)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-60}=\frac{-2}{-120}
=1/60
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-60}=\frac{0}{-120}
=0
$