5+7/2h=6+9/4h

Solution for 5+7/2h=6+9/4h equation:

5+7/2h=6+9/4h

We move all terms to the left:

5+7/2h-(6+9/4h)=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

7/2h-(9/4h+6)+5=0

We get rid of parentheses

7/2h-9/4h-6+5=0

We calculate fractions


28h/8h^2+(-18h)/8h^2-6+5=0

We add all the numbers together, and all the variables

28h/8h^2+(-18h)/8h^2-1=0

We multiply all the terms by the denominator


28h+(-18h)-1*8h^2=0

Wy multiply elements

-8h^2+28h+(-18h)=0

We get rid of parentheses

-8h^2+28h-18h=0

We add all the numbers together, and all the variables

-8h^2+10h=0

a = -8; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-8)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-8}=\frac{-20}{-16}
=1+1/4
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-8}=\frac{0}{-16}
=0
$