H(x)=1/x+5

Solution for H(x)=1/x+5 equation:

(H)=1/H+5

We move all terms to the left:

(H)-(1/H+5)=0


Domain of the equation: H+5)!=0

H∈R


We get rid of parentheses

H-1/H-5=0

We multiply all the terms by the denominator


H*H-5*H-1=0

We add all the numbers together, and all the variables

-5H+H*H-1=0

Wy multiply elements

H^2-5H-1=0

a = 1; b = -5; c = -1;
Δ = b2-4ac
Δ = -52-4·1·(-1)
Δ = 29
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{29}}{2*1}=\frac{5-\sqrt{29}}{2}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{29}}{2*1}=\frac{5+\sqrt{29}}{2}
$