h-(27/h)=6

Solution for h-(27/h)=6 equation:

h-(27/h)=6

We move all terms to the left:

h-(27/h)-(6)=0


Domain of the equation: h)!=0

h!=0/1

h!=0

h∈R


We add all the numbers together, and all the variables

h-(+27/h)-6=0

We get rid of parentheses

h-27/h-6=0

We multiply all the terms by the denominator


h*h-6*h-27=0

We add all the numbers together, and all the variables

-6h+h*h-27=0

Wy multiply elements

h^2-6h-27=0

a = 1; b = -6; c = -27;
Δ = b2-4ac
Δ = -62-4·1·(-27)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-12}{2*1}=\frac{-6}{2}
=-3
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+12}{2*1}=\frac{18}{2}
=9
$