2/3d-1/4d=-22

Solution for 2/3d-1/4d=-22 equation:

2/3d-1/4d=-22

We move all terms to the left:

2/3d-1/4d-(-22)=0


Domain of the equation: 3d!=0

d!=0/3

d!=0

d∈R



Domain of the equation: 4d!=0

d!=0/4

d!=0

d∈R


We add all the numbers together, and all the variables

2/3d-1/4d+22=0

We calculate fractions


8d/12d^2+(-3d)/12d^2+22=0

We multiply all the terms by the denominator


8d+(-3d)+22*12d^2=0

Wy multiply elements

264d^2+8d+(-3d)=0

We get rid of parentheses

264d^2+8d-3d=0

We add all the numbers together, and all the variables

264d^2+5d=0

a = 264; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·264·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*264}=\frac{-10}{528}
=-5/264
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*264}=\frac{0}{528}
=0
$