12h-1/4h=7/4h

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Solution for 12h-1/4h=7/4h equation:



12h-1/4h=7/4h
We move all terms to the left:
12h-1/4h-(7/4h)=0
Domain of the equation: 4h!=0
h!=0/4
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
12h-1/4h-(+7/4h)=0
We get rid of parentheses
12h-1/4h-7/4h=0
We multiply all the terms by the denominator
12h*4h-1-7=0
We add all the numbers together, and all the variables
12h*4h-8=0
Wy multiply elements
48h^2-8=0
a = 48; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·48·(-8)
Δ = 1536
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:
$\sqrt{\Delta}=\sqrt{1536}=\sqrt{256*6}=\sqrt{256}*\sqrt{6}=16\sqrt{6}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{6}}{2*48}=\frac{0-16\sqrt{6}}{96} =-\frac{16\sqrt{6}}{96} =-\frac{\sqrt{6}}{6} $
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{6}}{2*48}=\frac{0+16\sqrt{6}}{96} =\frac{16\sqrt{6}}{96} =\frac{\sqrt{6}}{6} $

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