2/3d+5=3/4d

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

2/3d+5=3/4d

We move all terms to the left:

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


Domain of the equation: 3d!=0

d!=0/3

d!=0

d∈R



Domain of the equation: 4d)!=0

d!=0/1

d!=0

d∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2/3d-3/4d+5=0

We calculate fractions


8d/12d^2+(-9d)/12d^2+5=0

We multiply all the terms by the denominator


8d+(-9d)+5*12d^2=0

Wy multiply elements

60d^2+8d+(-9d)=0

We get rid of parentheses

60d^2+8d-9d=0

We add all the numbers together, and all the variables

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