(-3d/4d+8)+2=5/d+2

Solution for (-3d/4d+8)+2=5/d+2 equation:

(-3d/4d+8)+2=5/d+2

We move all terms to the left:

(-3d/4d+8)+2-(5/d+2)=0


Domain of the equation: 4d+8)!=0

d∈R



Domain of the equation: d+2)!=0

d∈R


We get rid of parentheses

-3d/4d-5/d+8-2+2=0

We calculate fractions


(-3d^2)/4d^2+(-20d)/4d^2+8-2+2=0

We add all the numbers together, and all the variables

(-3d^2)/4d^2+(-20d)/4d^2+8=0

We multiply all the terms by the denominator


(-3d^2)+(-20d)+8*4d^2=0

Wy multiply elements

(-3d^2)+32d^2+(-20d)=0

We get rid of parentheses

-3d^2+32d^2-20d=0

We add all the numbers together, and all the variables

29d^2-20d=0

a = 29; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·29·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*29}=\frac{0}{58}
=0
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*29}=\frac{40}{58}
=20/29
$