1/3h-4(2/3h-3)=60

Solution for 1/3h-4(2/3h-3)=60 equation:

1/3h-4(2/3h-3)=60

We move all terms to the left:

1/3h-4(2/3h-3)-(60)=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+12-60=0

We multiply all the terms by the denominator


-8h*3h+12*3h-60*3h+1=0

Wy multiply elements

-24h^2+36h-180h+1=0

We add all the numbers together, and all the variables

-24h^2-144h+1=0

a = -24; b = -144; c = +1;
Δ = b2-4ac
Δ = -1442-4·(-24)·1
Δ = 20832
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:

$\sqrt{\Delta}=\sqrt{20832}=\sqrt{16*1302}=\sqrt{16}*\sqrt{1302}=4\sqrt{1302}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-4\sqrt{1302}}{2*-24}=\frac{144-4\sqrt{1302}}{-48}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+4\sqrt{1302}}{2*-24}=\frac{144+4\sqrt{1302}}{-48}
$