3/8h+19=8/3h+32

Solution for 3/8h+19=8/3h+32 equation:

3/8h+19=8/3h+32

We move all terms to the left:

3/8h+19-(8/3h+32)=0


Domain of the equation: 8h!=0

h!=0/8

h!=0

h∈R



Domain of the equation: 3h+32)!=0

h∈R


We get rid of parentheses

3/8h-8/3h-32+19=0

We calculate fractions


9h/24h^2+(-64h)/24h^2-32+19=0

We add all the numbers together, and all the variables

9h/24h^2+(-64h)/24h^2-13=0

We multiply all the terms by the denominator


9h+(-64h)-13*24h^2=0

Wy multiply elements

-312h^2+9h+(-64h)=0

We get rid of parentheses

-312h^2+9h-64h=0

We add all the numbers together, and all the variables

-312h^2-55h=0

a = -312; b = -55; c = 0;
Δ = b2-4ac
Δ = -552-4·(-312)·0
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-55}{2*-312}=\frac{0}{-624}
=0
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+55}{2*-312}=\frac{110}{-624}
=-55/312
$