23h-1/3h+11=8

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Solution for 23h-1/3h+11=8 equation:



23h-1/3h+11=8
We move all terms to the left:
23h-1/3h+11-(8)=0
Domain of the equation: 3h!=0
h!=0/3
h!=0
h∈R
We add all the numbers together, and all the variables
23h-1/3h+3=0
We multiply all the terms by the denominator
23h*3h+3*3h-1=0
Wy multiply elements
69h^2+9h-1=0
a = 69; b = 9; c = -1;
Δ = b2-4ac
Δ = 92-4·69·(-1)
Δ = 357
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{357}}{2*69}=\frac{-9-\sqrt{357}}{138} $
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{357}}{2*69}=\frac{-9+\sqrt{357}}{138} $

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