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

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

We multiply all the terms by the denominator


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

Wy multiply elements

-9h^2+6h+2=0

a = -9; b = 6; c = +2;
Δ = b2-4ac
Δ = 62-4·(-9)·2
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{3}}{2*-9}=\frac{-6-6\sqrt{3}}{-18}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{3}}{2*-9}=\frac{-6+6\sqrt{3}}{-18}
$