H(x)=8/x+5

Solution for H(x)=8/x+5 equation:

(H)=8/H+5

We move all terms to the left:

(H)-(8/H+5)=0


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

H∈R


We get rid of parentheses

H-8/H-5=0

We multiply all the terms by the denominator


H*H-5*H-8=0

We add all the numbers together, and all the variables

-5H+H*H-8=0

Wy multiply elements

H^2-5H-8=0

a = 1; b = -5; c = -8;
Δ = b2-4ac
Δ = -52-4·1·(-8)
Δ = 57
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{57}}{2*1}=\frac{5-\sqrt{57}}{2}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{57}}{2*1}=\frac{5+\sqrt{57}}{2}
$