(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: 4)h!=0

h!=0/1

h!=0

h∈R



Domain of the equation: 2)h!=0

h!=0/1

h!=0

h∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses

h^2+3h^2+h^2-3=0

We add all the numbers together, and all the variables

5h^2-3=0

a = 5; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·5·(-3)
Δ = 60
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{15}}{2*5}=\frac{0-2\sqrt{15}}{10}
=-\frac{2\sqrt{15}}{10}
=-\frac{\sqrt{15}}{5}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{15}}{2*5}=\frac{0+2\sqrt{15}}{10}
=\frac{2\sqrt{15}}{10}
=\frac{\sqrt{15}}{5}
$