1/4h+3/4+1/2h+2=5

Solution for 1/4h+3/4+1/2h+2=5 equation:

1/4h+3/4+1/2h+2=5

We move all terms to the left:

1/4h+3/4+1/2h+2-(5)=0


Domain of the equation: 4h!=0

h!=0/4

h!=0

h∈R



Domain of the equation: 2h!=0

h!=0/2

h!=0

h∈R


determiningTheFunctionDomain
1/4h+1/2h+2-5+3/4=0

We add all the numbers together, and all the variables

1/4h+1/2h-3+3/4=0

We calculate fractions


2h/128h^2+64h/128h^2+6h/128h^2-3=0

We multiply all the terms by the denominator


2h+64h+6h-3*128h^2=0

We add all the numbers together, and all the variables

72h-3*128h^2=0

Wy multiply elements

-384h^2+72h=0

a = -384; b = 72; c = 0;
Δ = b2-4ac
Δ = 722-4·(-384)·0
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-72}{2*-384}=\frac{-144}{-768}
=3/16
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+72}{2*-384}=\frac{0}{-768}
=0
$