2/3h-1/4h=6

Solution for 2/3h-1/4h=6 equation:

2/3h-1/4h=6

We move all terms to the left:

2/3h-1/4h-(6)=0


Domain of the equation: 3h!=0

h!=0/3

h!=0

h∈R



Domain of the equation: 4h!=0

h!=0/4

h!=0

h∈R


We calculate fractions


8h/12h^2+(-3h)/12h^2-6=0

We multiply all the terms by the denominator


8h+(-3h)-6*12h^2=0

Wy multiply elements

-72h^2+8h+(-3h)=0

We get rid of parentheses

-72h^2+8h-3h=0

We add all the numbers together, and all the variables

-72h^2+5h=0

a = -72; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-72)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-72}=\frac{-10}{-144}
=5/72
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-72}=\frac{0}{-144}
=0
$