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

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}
$