5/3d+2/3=5+d/2d

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

5/3d+2/3=5+d/2d

We move all terms to the left:

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


Domain of the equation: 3d!=0

d!=0/3

d!=0

d∈R



Domain of the equation: 2d)!=0

d!=0/1

d!=0

d∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-27d^2)/54d^2+10d/54d^2+4d/54d^2-5=0

We multiply all the terms by the denominator


(-27d^2)+10d+4d-5*54d^2=0

We add all the numbers together, and all the variables

(-27d^2)+14d-5*54d^2=0

Wy multiply elements

(-27d^2)-270d^2+14d=0

We get rid of parentheses

-27d^2-270d^2+14d=0

We add all the numbers together, and all the variables

-297d^2+14d=0

a = -297; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-297)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-297}=\frac{-28}{-594}
=14/297
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-297}=\frac{0}{-594}
=0
$