2/3h-13h+11=8

Solution for 2/3h-13h+11=8 equation:

2/3h-13h+11=8

We move all terms to the left:

2/3h-13h+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

-13h+2/3h+3=0

We multiply all the terms by the denominator


-13h*3h+3*3h+2=0

Wy multiply elements

-39h^2+9h+2=0

a = -39; b = 9; c = +2;
Δ = b2-4ac
Δ = 92-4·(-39)·2
Δ = 393
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{393}}{2*-39}=\frac{-9-\sqrt{393}}{-78}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{393}}{2*-39}=\frac{-9+\sqrt{393}}{-78}
$