H(6)=x-8/3x+6

Solution for H(6)=x-8/3x+6 equation:

(6)=H-8/3H+6

We move all terms to the left:

(6)-(H-8/3H+6)=0


Domain of the equation: 3H+6)!=0

H∈R


We get rid of parentheses

-H+8/3H-6+6=0

We multiply all the terms by the denominator


-H*3H-6*3H+6*3H+8=0

Wy multiply elements

-3H^2-18H+18H+8=0

We add all the numbers together, and all the variables

-3H^2+8=0

a = -3; b = 0; c = +8;
Δ = b2-4ac
Δ = 02-4·(-3)·8
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{6}}{2*-3}=\frac{0-4\sqrt{6}}{-6}
=-\frac{4\sqrt{6}}{-6}
=-\frac{2\sqrt{6}}{-3}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{6}}{2*-3}=\frac{0+4\sqrt{6}}{-6}
=\frac{4\sqrt{6}}{-6}
=\frac{2\sqrt{6}}{-3}
$