-(2.666666666666h-12)=1/3h-6

Solution for -(2.666666666666h-12)=1/3h-6 equation:

-(2.666666666666h-12)=1/3h-6

We move all terms to the left:

-(2.666666666666h-12)-(1/3h-6)=0


Domain of the equation: 3h-6)!=0

h∈R


We get rid of parentheses

-2.666666666666h-1/3h+12+6=0

We multiply all the terms by the denominator


-(2.666666666666h)*3h+12*3h+6*3h-1=0

We add all the numbers together, and all the variables

-(+2.666666666666h)*3h+12*3h+6*3h-1=0

We multiply parentheses

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

Wy multiply elements

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

We add all the numbers together, and all the variables

-6h^2+54h-1=0

a = -6; b = 54; c = -1;
Δ = b2-4ac
Δ = 542-4·(-6)·(-1)
Δ = 2892
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:

$\sqrt{\Delta}=\sqrt{2892}=\sqrt{4*723}=\sqrt{4}*\sqrt{723}=2\sqrt{723}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{723}}{2*-6}=\frac{-54-2\sqrt{723}}{-12}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{723}}{2*-6}=\frac{-54+2\sqrt{723}}{-12}
$