23h-1/3h+11=8

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}
$