1/3h+1/5h=1

Solution for 1/3h+1/5h=1 equation:

1/3h+1/5h=1

We move all terms to the left:

1/3h+1/5h-(1)=0


Domain of the equation: 3h!=0

h!=0/3

h!=0

h∈R



Domain of the equation: 5h!=0

h!=0/5

h!=0

h∈R


We calculate fractions


5h/15h^2+3h/15h^2-1=0

We multiply all the terms by the denominator


5h+3h-1*15h^2=0

We add all the numbers together, and all the variables

8h-1*15h^2=0

Wy multiply elements

-15h^2+8h=0

a = -15; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-15)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-15}=\frac{-16}{-30}
=8/15
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-15}=\frac{0}{-30}
=0
$