2/3d+5=20+d

Solution for 2/3d+5=20+d equation:

2/3d+5=20+d

We move all terms to the left:

2/3d+5-(20+d)=0


Domain of the equation: 3d!=0

d!=0/3

d!=0

d∈R


We add all the numbers together, and all the variables

2/3d-(d+20)+5=0

We get rid of parentheses

2/3d-d-20+5=0

We multiply all the terms by the denominator


-d*3d-20*3d+5*3d+2=0

Wy multiply elements

-3d^2-60d+15d+2=0

We add all the numbers together, and all the variables

-3d^2-45d+2=0

a = -3; b = -45; c = +2;
Δ = b2-4ac
Δ = -452-4·(-3)·2
Δ = 2049
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-\sqrt{2049}}{2*-3}=\frac{45-\sqrt{2049}}{-6}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2049}}{2*-3}=\frac{45+\sqrt{2049}}{-6}
$