2/3h-9=2h+3

Solution for 2/3h-9=2h+3 equation:

2/3h-9=2h+3

We move all terms to the left:

2/3h-9-(2h+3)=0


Domain of the equation: 3h!=0

h!=0/3

h!=0

h∈R


We get rid of parentheses

2/3h-2h-3-9=0

We multiply all the terms by the denominator


-2h*3h-3*3h-9*3h+2=0

Wy multiply elements

-6h^2-9h-27h+2=0

We add all the numbers together, and all the variables

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

a = -6; b = -36; c = +2;
Δ = b2-4ac
Δ = -362-4·(-6)·2
Δ = 1344
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:

$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-8\sqrt{21}}{2*-6}=\frac{36-8\sqrt{21}}{-12}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+8\sqrt{21}}{2*-6}=\frac{36+8\sqrt{21}}{-12}
$