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

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

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

We move all terms to the left:

(1)/(4)h+(3)/(4)h+(1)/(2)h+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


We add all the numbers together, and all the variables

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

We calculate fractions


(6h+1)/8h^2+4h/8h^2-3=0

We multiply all the terms by the denominator


(6h+1)+4h-3*8h^2=0

We add all the numbers together, and all the variables

4h+(6h+1)-3*8h^2=0

Wy multiply elements

-24h^2+4h+(6h+1)=0

We get rid of parentheses

-24h^2+4h+6h+1=0

We add all the numbers together, and all the variables

-24h^2+10h+1=0

a = -24; b = 10; c = +1;
Δ = b2-4ac
Δ = 102-4·(-24)·1
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-14}{2*-24}=\frac{-24}{-48}
=1/2
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+14}{2*-24}=\frac{4}{-48}
=-1/12
$