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-6-2/3d+13/6d=-4
We move all terms to the left:
-6-2/3d+13/6d-(-4)=0
Domain of the equation: 3d!=0
d!=0/3
d!=0
d∈R
Domain of the equation: 6d!=0We add all the numbers together, and all the variables
d!=0/6
d!=0
d∈R
-2/3d+13/6d-2=0
We calculate fractions
(-12d)/18d^2+39d/18d^2-2=0
We multiply all the terms by the denominator
(-12d)+39d-2*18d^2=0
We add all the numbers together, and all the variables
39d+(-12d)-2*18d^2=0
Wy multiply elements
-36d^2+39d+(-12d)=0
We get rid of parentheses
-36d^2+39d-12d=0
We add all the numbers together, and all the variables
-36d^2+27d=0
a = -36; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-36)·0
Δ = 729
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{729}=27$$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-36}=\frac{-54}{-72} =3/4 $$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-36}=\frac{0}{-72} =0 $
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