2/3*h+2=h

Solution for 2/3*h+2=h equation:

2/3h+2=h

We move all terms to the left:

2/3h+2-(h)=0


Domain of the equation: 3h!=0

h!=0/3

h!=0

h∈R


We add all the numbers together, and all the variables

-1h+2/3h+2=0

We multiply all the terms by the denominator


-1h*3h+2*3h+2=0

Wy multiply elements

-3h^2+6h+2=0

a = -3; b = 6; c = +2;
Δ = b2-4ac
Δ = 62-4·(-3)·2
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{15}}{2*-3}=\frac{-6-2\sqrt{15}}{-6}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{15}}{2*-3}=\frac{-6+2\sqrt{15}}{-6}
$