42+7d=21(1/3d+2)

Solution for 42+7d=21(1/3d+2) equation:

42+7d=21(1/3d+2)

We move all terms to the left:

42+7d-(21(1/3d+2))=0


Domain of the equation: 3d+2))!=0

d∈R


We multiply all the terms by the denominator


7d*3d+42*3d+2))-(21(1+2))=0

We add all the numbers together, and all the variables

7d*3d+42*3d+2))-(213)=0

We add all the numbers together, and all the variables

7d*3d+42*3d=0

Wy multiply elements

21d^2+126d=0

a = 21; b = 126; c = 0;
Δ = b2-4ac
Δ = 1262-4·21·0
Δ = 15876
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15876}=126$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-126}{2*21}=\frac{-252}{42}
=-6
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+126}{2*21}=\frac{0}{42}
=0
$