2.3h-1/3h+11=8

Solution for 2.3h-1/3h+11=8 equation:

2.3h-1/3h+11=8

We move all terms to the left:

2.3h-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

2.3h-1/3h+3=0

We multiply all the terms by the denominator


(2.3h)*3h+3*3h-1=0

We add all the numbers together, and all the variables

(+2.3h)*3h+3*3h-1=0

We multiply parentheses

6h^2+3*3h-1=0

Wy multiply elements

6h^2+9h-1=0

a = 6; b = 9; c = -1;
Δ = b2-4ac
Δ = 92-4·6·(-1)
Δ = 105
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{105}}{2*6}=\frac{-9-\sqrt{105}}{12}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{105}}{2*6}=\frac{-9+\sqrt{105}}{12}
$