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1/3h+5=1/6h+1
We move all terms to the left:
1/3h+5-(1/6h+1)=0
Domain of the equation: 3h!=0
h!=0/3
h!=0
h∈R
Domain of the equation: 6h+1)!=0We get rid of parentheses
h∈R
1/3h-1/6h-1+5=0
We calculate fractions
6h/18h^2+(-3h)/18h^2-1+5=0
We add all the numbers together, and all the variables
6h/18h^2+(-3h)/18h^2+4=0
We multiply all the terms by the denominator
6h+(-3h)+4*18h^2=0
Wy multiply elements
72h^2+6h+(-3h)=0
We get rid of parentheses
72h^2+6h-3h=0
We add all the numbers together, and all the variables
72h^2+3h=0
a = 72; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·72·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{9}=3$$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*72}=\frac{-6}{144} =-1/24 $$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*72}=\frac{0}{144} =0 $
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