1/5h+1/2h=1/4

Solution for 1/5h+1/2h=1/4 equation:

1/5h+1/2h=1/4

We move all terms to the left:

1/5h+1/2h-(1/4)=0


Domain of the equation: 5h!=0

h!=0/5

h!=0

h∈R



Domain of the equation: 2h!=0

h!=0/2

h!=0

h∈R


We add all the numbers together, and all the variables

1/5h+1/2h-(+1/4)=0

We get rid of parentheses

1/5h+1/2h-1/4=0

We calculate fractions


(-20h^2)/160h^2+32h/160h^2+80h/160h^2=0

We multiply all the terms by the denominator


(-20h^2)+32h+80h=0

We add all the numbers together, and all the variables

(-20h^2)+112h=0

We get rid of parentheses

-20h^2+112h=0

a = -20; b = 112; c = 0;
Δ = b2-4ac
Δ = 1122-4·(-20)·0
Δ = 12544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12544}=112$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-112}{2*-20}=\frac{-224}{-40}
=5+3/5
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+112}{2*-20}=\frac{0}{-40}
=0
$