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))=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=0

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -24; b = 36; c = +1;
Δ = b2-4ac
Δ = 362-4·(-24)·1
Δ = 1392
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:

$\sqrt{\Delta}=\sqrt{1392}=\sqrt{16*87}=\sqrt{16}*\sqrt{87}=4\sqrt{87}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{87}}{2*-24}=\frac{-36-4\sqrt{87}}{-48}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{87}}{2*-24}=\frac{-36+4\sqrt{87}}{-48}
$