2/3h+3/4h=4/7

Solution for 2/3h+3/4h=4/7 equation:

2/3h+3/4h=4/7

We move all terms to the left:

2/3h+3/4h-(4/7)=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 add all the numbers together, and all the variables

2/3h+3/4h-(+4/7)=0

We get rid of parentheses

2/3h+3/4h-4/7=0

We calculate fractions


(-192h^2)/588h^2+392h/588h^2+441h/588h^2=0

We multiply all the terms by the denominator


(-192h^2)+392h+441h=0

We add all the numbers together, and all the variables

(-192h^2)+833h=0

We get rid of parentheses

-192h^2+833h=0

a = -192; b = 833; c = 0;
Δ = b2-4ac
Δ = 8332-4·(-192)·0
Δ = 693889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{693889}=833$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(833)-833}{2*-192}=\frac{-1666}{-384}
=4+65/192
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(833)+833}{2*-192}=\frac{0}{-384}
=0
$