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1/3h=6,h=2

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Solution for 1/3h=6,h=2 equation:



1/3h=6.h=2
We move all terms to the left:
1/3h-(6.h)=0
Domain of the equation: 3h!=0
h!=0/3
h!=0
h∈R
We add all the numbers together, and all the variables
1/3h-(+6.h)=0
We get rid of parentheses
1/3h-6.h=0
We multiply all the terms by the denominator
-(6.h)*3h+1=0
We add all the numbers together, and all the variables
-(+6.h)*3h+1=0
We multiply parentheses
-18h^2+1=0
a = -18; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-18)·1
Δ = 72
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}

The end solution:
\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}
h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{2}}{2*-18}=\frac{0-6\sqrt{2}}{-36} =-\frac{6\sqrt{2}}{-36} =-\frac{\sqrt{2}}{-6}
h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{2}}{2*-18}=\frac{0+6\sqrt{2}}{-36} =\frac{6\sqrt{2}}{-36} =\frac{\sqrt{2}}{-6}

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