1/3h-h(2/3h-3)=2/3-6

Solution for 1/3h-h(2/3h-3)=2/3-6 equation:

1/3h-h(2/3h-3)=2/3-6

We move all terms to the left:

1/3h-h(2/3h-3)-(2/3-6)=0


Domain of the equation: 3h!=0

h!=0/3

h!=0

h∈R



Domain of the equation: 3h-3)!=0

h∈R


We multiply parentheses

-2h^2+1/3h+3h-(2/3-6)=0

We get rid of parentheses

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

We calculate fractions


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

a = -2; b = 3; c = +6;
Δ = b2-4ac
Δ = 32-4·(-2)·6
Δ = 57
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{-(3)-\sqrt{57}}{2*-2}=\frac{-3-\sqrt{57}}{-4}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{57}}{2*-2}=\frac{-3+\sqrt{57}}{-4}
$