H(x)=9x/x+8

Solution for H(x)=9x/x+8 equation:

(H)=9H/H+8

We move all terms to the left:

(H)-(9H/H+8)=0


Domain of the equation: H+8)!=0

H∈R


We get rid of parentheses

H-9H/H-8=0

We multiply all the terms by the denominator


H*H-9H-8*H=0

We add all the numbers together, and all the variables

-17H+H*H=0

Wy multiply elements

H^2-17H=0

a = 1; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·1·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*1}=\frac{0}{2}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*1}=\frac{34}{2}
=17
$