1/8h+6-3/4h=0

Solution for 1/8h+6-3/4h=0 equation:

1/8h+6-3/4h=0


Domain of the equation: 8h!=0

h!=0/8

h!=0

h∈R



Domain of the equation: 4h!=0

h!=0/4

h!=0

h∈R


We calculate fractions


4h/32h^2+(-24h)/32h^2+6=0

We multiply all the terms by the denominator


4h+(-24h)+6*32h^2=0

Wy multiply elements

192h^2+4h+(-24h)=0

We get rid of parentheses

192h^2+4h-24h=0

We add all the numbers together, and all the variables

192h^2-20h=0

a = 192; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·192·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*192}=\frac{0}{384}
=0
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*192}=\frac{40}{384}
=5/48
$