5+31/2h=6+21/4h

Solution for 5+31/2h=6+21/4h equation:

5+31/2h=6+21/4h

We move all terms to the left:

5+31/2h-(6+21/4h)=0


Domain of the equation: 2h!=0

h!=0/2

h!=0

h∈R



Domain of the equation: 4h)!=0

h!=0/1

h!=0

h∈R


We add all the numbers together, and all the variables

31/2h-(21/4h+6)+5=0

We get rid of parentheses

31/2h-21/4h-6+5=0

We calculate fractions


124h/8h^2+(-42h)/8h^2-6+5=0

We add all the numbers together, and all the variables

124h/8h^2+(-42h)/8h^2-1=0

We multiply all the terms by the denominator


124h+(-42h)-1*8h^2=0

Wy multiply elements

-8h^2+124h+(-42h)=0

We get rid of parentheses

-8h^2+124h-42h=0

We add all the numbers together, and all the variables

-8h^2+82h=0

a = -8; b = 82; c = 0;
Δ = b2-4ac
Δ = 822-4·(-8)·0
Δ = 6724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6724}=82$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(82)-82}{2*-8}=\frac{-164}{-16}
=10+1/4
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(82)+82}{2*-8}=\frac{0}{-16}
=0
$