1/3h-4(2/3h)=-6

Solution for 1/3h-4(2/3h)=-6 equation:

1/3h-4(2/3h)=-6

We move all terms to the left:

1/3h-4(2/3h)-(-6)=0


Domain of the equation: 3h!=0

h!=0/3

h!=0

h∈R



Domain of the equation: 3h)!=0

h!=0/1

h!=0

h∈R


We add all the numbers together, and all the variables

1/3h-4(+2/3h)-(-6)=0

We add all the numbers together, and all the variables

1/3h-4(+2/3h)+6=0

We multiply parentheses

1/3h-8h+6=0

We multiply all the terms by the denominator


-8h*3h+6*3h+1=0

Wy multiply elements

-24h^2+18h+1=0

a = -24; b = 18; c = +1;
Δ = b2-4ac
Δ = 182-4·(-24)·1
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{105}}{2*-24}=\frac{-18-2\sqrt{105}}{-48}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{105}}{2*-24}=\frac{-18+2\sqrt{105}}{-48}
$