1/3h-4(2/3h-3)=2.3h-6

Solution for 1/3h-4(2/3h-3)=2.3h-6 equation:

1/3h-4(2/3h-3)=2.3h-6

We move all terms to the left:

1/3h-4(2/3h-3)-(2.3h-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

1/3h-8h-(2.3h-6)+12=0

We get rid of parentheses

1/3h-8h-2.3h+6+12=0

We multiply all the terms by the denominator


-8h*3h-(2.3h)*3h+6*3h+12*3h+1=0

We add all the numbers together, and all the variables

-8h*3h-(+2.3h)*3h+6*3h+12*3h+1=0

We multiply parentheses

-6h^2-8h*3h+6*3h+12*3h+1=0

Wy multiply elements

-6h^2-24h^2+18h+36h+1=0

We add all the numbers together, and all the variables

-30h^2+54h+1=0

a = -30; b = 54; c = +1;
Δ = b2-4ac
Δ = 542-4·(-30)·1
Δ = 3036
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:

$\sqrt{\Delta}=\sqrt{3036}=\sqrt{4*759}=\sqrt{4}*\sqrt{759}=2\sqrt{759}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{759}}{2*-30}=\frac{-54-2\sqrt{759}}{-60}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{759}}{2*-30}=\frac{-54+2\sqrt{759}}{-60}
$