-8/12d-3/21d=-22

Solution for -8/12d-3/21d=-22 equation:

-8/12d-3/21d=-22

We move all terms to the left:

-8/12d-3/21d-(-22)=0


Domain of the equation: 12d!=0

d!=0/12

d!=0

d∈R



Domain of the equation: 21d!=0

d!=0/21

d!=0

d∈R


We add all the numbers together, and all the variables

-8/12d-3/21d+22=0

We calculate fractions


(-168d)/252d^2+(-36d)/252d^2+22=0

We multiply all the terms by the denominator


(-168d)+(-36d)+22*252d^2=0

Wy multiply elements

5544d^2+(-168d)+(-36d)=0

We get rid of parentheses

5544d^2-168d-36d=0

We add all the numbers together, and all the variables

5544d^2-204d=0

a = 5544; b = -204; c = 0;
Δ = b2-4ac
Δ = -2042-4·5544·0
Δ = 41616
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{41616}=204$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-204)-204}{2*5544}=\frac{0}{11088}
=0
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-204)+204}{2*5544}=\frac{408}{11088}
=17/462
$